You know what I’m about to say, but to reiterate: this is a tricky one. Archery is weirdly undersupported in 3.5e, and either Charisma or Wisdom would lend itself much better to this style of character (both can be used for archery, with Charming the Arrow or Zen Archery, respectively). So, a challenge!
Getting your spells
Intelligence is, sort of weirdly, not used by all that many spellcasters. Wizards are the big, obvious one, the first spellcasters to come to mind for many, but after that there is... not a whole lot.
Wizard: almost-certainly what you’re going to go with, and almost-certainly the best. They get the best spells in the game, and they use Intelligence: everything you wanted. Also, they have a useful ACF from Unearthed Arcana to allow them to get fighter bonus feats—nice!
Archivist:[HoH] an “archer-vist” is certainly a thing, but it relies on Wisdom and Zen Archery—because archivists are split between Intelligence and Wisdom. Aside from that, basically a divine wizard. Not very useful here, with poor Wisdom.
Artificer:[EbCS] you could. They’re certainly powerful enough. And you can arguably afford more multiclassing than wizard, and you get more BAB and skills. The problem is that playing an artificer well requires an incredible amount of work. I like to say that step 1 of playing an artificer well is “become a certified public accountant.” I’m not prepared to do that work for myself, much less for anyone else.
Wu Jen:[CArc] the wizard’s weird cousin. Intelligence-based, preparing-from-spellbooks spellcaster. Decent spell list, but it pales in comparison to the wizard’s. Class features are kind of interesting but nothing stellar.
Psion:[XPH] Intelligence-based, and psionics is pretty similar to spontaneous spellcasting. The erudite variant in Complete Psionic gets to be more prepared. Either way, some powerful options here (e.g. control body yourself, solicit psicrystal to free your actions, and now everything you do is Intelligence-based), but it’s not “spellcasting.”
Assassin: fitting, not terrible, spontaneous Intelligence-based spellcaster. With Spell Compendium, there are some pretty good assassin spells out there, but ultimately you want better spells than this.
Beholder Mage:[LoM] no. Just, no. You’re just going to get yourself uninvited from the game.
Realistically, wizard is what I’m assuming you go with. Artificer and psion have things to recommend them, and assassin could make for a really stylish option in a low-power game, but the question is tagged wizard and wizard truly probably the best.
Diviner is fine as an option, and appropriate. You might take a look at this Q&A for more about choosing specialty and related options, but the tl;dr here is that a diviner prohibiting enchantment is probably your best bet. Master diviner[CMage] would be nice, but you don’t really have the feats for it and you won’t have the levels.
Getting your archery
You already have a level of fighter—you definitely don’t want any more. Even that one wasn’t great, but we can do some useful things with it—especially if you can take some variants. But at this point, what we are concerned about are feats and weapons.
If you can, ask to retrain or retcon your fighter level to include the hit ‘n’ run tactics variant.[DotU] Hit ‘n’ run tactics gives you +2 to Initiative and lets you add your Dexterity to damage against flat-footed foes, which is a big deal.
Feats you absolutely want: Point Blank Shot, Precise Shot, Rapid Shot, Knowledge Devotion,[CChamp] Dead Eye[DrComp] (note that errata changed the requirement from BAB +14 to BAB +1 (!)).
Feats you might want: Hand Crossbow Focus,[DotU] Crossbow Sniper.[PHB2]
Note that wizard can help you get these feats.
Basically, the question here is what weapon you want to use. Crossbows require Rapid Reload (or similar, see below) to do anything useful with them, but open up the option of getting Crossbow Sniper, which adds half your Dexterity bonus to damage. You should already have it once from Dead Eye, and possibly once again from hit ‘n’ run tactics if your target is flat-footed. With your high Dexterity, applying it multiple times is a very good thing.
Just go with a longbow if you’re going to use a bow—the greatbow[CWar] exists, but it isn’t worth a feat, or even worth the aptitude property (see below). Even if you had it, you’ll prefer the energy bow once you can get it (see below).
For crossbows, you really have two options: light crossbows or hand crossbows. Heavy and great crossbows[AEG] are out because of their lengthy loading time even with Rapid Reload (but see more on that under aptitude, below). The advantage of hand crossbows is that Hand Crossbow Focus exists. It’s Weapon Focus (hand crossbow) except it also allows you to reload hand crossbows as a free action, so you don’t need to get Rapid Reload. Since Weapon Focus is necessary in a number of cases, you might as well get Rapid Reload at the same time and open up the option of Crossbow Sniper in the future. Unfortunately, you have to spend a feat on Exotic Weapon Proficiency (hand crossbow) to qualify for Hand Crossbow Focus, so even if you need Weapon Focus with something, this doesn’t actually save you feats: Weapon Focus (light crossbow) + Rapid Reload vs. Exotic Weapon Proficiency (hand crossbow) + Hand Crossbow Focus amounts to the same thing, and one more feat than bows would use in the same situation. If you don’t need Weapon Focus, light crossbows are probably better just because of the feat cost—hand crossbows do have some marginal advantages, but nothing worth a feat.
If you don’t go with knight phantom (see below), you might alternatively go with the exoticist fighter variant,[Dr 310] to get four exotic weapon proficiencies, including a hand crossbow. This costs martial weapon proficiency, so it prevents knight phantom. The other three proficiencies don’t really matter—you could get greatbow proficiency, I guess, if you aren’t doing knight phantom, energy bow, or Crossbow Sniper.
Getting magic in your bows
Magic weapons are obviously something important to you. There are many options you could select, but there are a few things to highlight:
Splitting[CoR] causes a weapon’s projectiles to split in two, doubling your attacks. This is incredibly potent, and easily worth the +3-equivalent price tag.
Hank’s energy bow[BtBoSM] is the best bow in the game, and the reason you wouldn’t actually use greatbow proficiency. It works like an automatically-adjusting composite longbow, and also generates its own arrows—which are made of force, which makes them extremely effective against a wide variety of foes (ignores DR, incorporeality, etc.). Most importantly, you get a benefit similar to Power Attack with it. That will be the source of a lot of damage for you.
Aptitude[ToB] is extremely controversial—it allows you to use the weapon proficiently even if you aren’t proficient with that type of weapon, and it also allows your feats that work with some other kind of weapon to also work on the aptitude weapon. Which means that a +1 aptitude great crossbow works with Hand Crossbow Focus—getting the +1 to attacks, and also the ability to reload as a free action (which Rapid Reload does not offer to great crossbows, and cannot be achieved any other way). Since great crossbows do massive damage, this is extremely potent. Ask your DM before you do it, though. It’s second only to using a +1 aptitude kukri with Lightning Maces[CWar] and Roundabout Kick[CWar] for cheesiest application of aptitude. Note that even if you do it, you still won’t need great crossbow proficiency since aptitude covers that too.
See also this answer about a Wisdom-based goliath sniper—many of the magical and otherwise “fancy” arrows mentioned therein are quite good for you as well, as are many of the other properties you might put on the bow itself.
Ultimately, a +1 aptitude splitting great crossbow used with Hand Crossbow Focus is the best option here, but it’s also quite abusive. The energy bow is vastly more reasonable, while still being quite strong—and yes, you can make a splitting energy bow and so on. A +1 splitting hand crossbow or +1 splitting light crossbow is also strong with Crossbow Sniper and enough Dexterity, but the energy bow is better. If you can’t get the energy bow, though, the (non-great) crossbows look a lot more competitive compared to a typical +1 splitting composite longbow. Additional special weapon properties over and above splitting (and aptitude if applicable) are, obviously, good once you can afford them.
Getting magic in your archery
Divinations to improve your archery are a great idea. Stealing from that goliath sniper answer, some really strong options:
Guided shot[CAdv] lets you ignore cover and penalties due to range.
Hunter’s eye[PHB2] gets you sneak attack damage, +1d6 per 3 caster levels. Not a sorcerer/wizard spell—see unseen seer below.
Sniper’s shot[SpComp] eliminates the range limit on sneak attack, such as from hunter’s eye.
See invisibility lets you, ya know, see invisible things. Very valuable.
Arcane sight lets you see magic, which is valuable for being aware of a lot of the most dangerous threats.
Telepathic bond is the best communication option available in the game.
True seeing is pricey, but extremely potent. Probably better off getting a scout’s headband for this, but still.
Moment of prescience and foresight are some of the best defensive buffs in the game.
Also, don’t forget non-divination mainstays like haste, nerveskitter,[SpComp] and so on, as well as non-combat divinations like scrying, contact other plane, and legend lore.
As for being an excellent combat-diviner, the unseen seer prestige class is for you.[CMage] It grants 7½/10 BAB, 10/10 spellcasting, improved divination caster level (at the cost of caster level for your other spells), and the ability to get some non-sor/wiz spells—like hunter’s eye. It also improves your precision damage bonuses—like sneak attack—so your hunter’s eye will actually be a little bit better, too.
Getting your mount
OK, at this point, you have the base of your spellcasting, you have archery-related feats, and you have your weapon. You’re also still a 1st-level fighter/1st-level diviner. Where else are you going to spend levels? Can you get a mount out of it?
Yes, you can! Of course. The best, most thematic option here is the knight phantom.[5N] That’s Eberron-specific, and within Eberron it’s specific to the country of Aundair and the Order of the Knights Arcane, which is a part of the Aundair military. Assuming your genasi isn’t a member, ask your DM about adapting it. The knight phantom is all about phantom steed, which is an excellent mount. It also provides 10/10 BAB and 9/10 spellcasting, which is solid enough.
Even if you don’t go with knight phantom, phantom steed is still an excellent option for mount.
Outside of that, your options are rather limited. Wild Cohort is probably your best bet, and that’s not a great bet. Arcane hierophant[RotW] would be pretty good—get a real animal companion—but it requires more levels of druid than you’re ever going to want.
Getting it all together
OK, so you now have a character with one level of fighter, at least one level of diviner, and you’re planning on some combination of knight phantom and unseen seer. You’re aiming for all the archery feats, and you know what weapon you’re looking for. What do you do with the rest of your levels? How do you use this all as well as possible?
First up, levels. As already mentioned, you don’t want more levels of fighter. Unseen seer requires you be 5th level before you qualify (since it requires 8 ranks in several skills), and knight phantom requires 6th (since you need phantom steed, a 3rd-level spell, as well as proficiency in all martial weapons). So you need more base class levels. That’s going to just be wizard—it’s the only way to get more wizard spellcasting. You could go with master specialist, but as mentioned that costs feats you don’t want to spend, and you aren’t going to take more than two levels of it.
So 1st-level fighter/4th-level wizard/5th-level unseen seer/10th-level knight phantom works as a plan. BAB +16/+11/+6/+1 is great, and the spellcasting of an 18th-level wizard is fantastic. You probably want to switch to knight phantom pretty early—either as soon as possible or as soon as you have hunter’s eye from unseen seer—and then go back to unseen seer after.
You could alternatively consider some abjurant champion[CMage] levels instead of unseen seer levels, or even knight phantom levels. After all, the knight phantom capstone doesn’t work on ranged weapons. Abjurant champion provides 5/5 BAB and 5/5 spellcasting, which is excellent. It also provides some great defensive bonuses when using abjurations. Don’t miss out on (greater) luminous armor[BoED] for upgrades to mage armor.
That path would mean a 1st-level fighter/4th-level diviner/5th-level unseen seer/7th-level knight phantom/3rd-level abjurant champion, or maybe 1st-level fighter/4th-level diviner/4th-level unseen seer/7th-level knight phantom/4th-level abjurant champion—depends whether you like arcane boost better than guarded mind or not.
If you can’t be a knight phantom, your best bet is probably 1st-level fighter/4th-level diviner/10th-level unseen seer/5th-level abjurant champion with phantom steed or Wild Cohort.
Unmarked entries are core, so mostly Player’s Handbook. All of them, at any rate, can be found in the SRD.
||Arms & Equipment Guide
||Beneath the Blade of Sun Mountain, one of the most obscure 3.5e supplements
||Champions of Ruin
||Drow of the Underdark (not to be confused with Underdark)
||Dragon magazine vol. 310
||Eberron Campaign Setting
||Heroes of Horror
||Player’s Handbook II
||Races of the Wild
||Tome of Battle: Book of the Nine Swords
||Expanded Psionics Handbook, also available on the SRD
Note that Hank’s energy bow, thankfully, is also available on Wizard’s website, since Beneath the Blade of Sun Mountain is the small pamphlet included with the D&D Cartoon DVD set, and very few people have that (I certainly don’t).
Also on Wizard’s website is the knight phantom, which may be convenient since it’s one of my most-highly-recommended classes for you.