Chaotic Good silverbrow human worshipper of Gruumsh, and ideally also of Milil. Yes, this is a bit strange, and is addressed in the answer, including alternatives.
Level |
Class |
Feat |
Bonus Feat (source) |
Special |
1st |
Harmonic Knight |
Dragonfire Inspiration |
Cleave (human), Point-blank Shot, Precise Shot (flaw) |
Inspire courage +1, 1/day |
2nd |
|
|
|
Divine grace |
3rd |
Warblade |
Stone Power |
|
Maneuvers |
4th |
Targeteer |
|
Rapid Shot (targeteer) |
Greatbow |
5th |
|
|
|
Arrow swarm |
6th |
Battle Howler of Gruumsh |
Song of the White Raven |
|
Bardic music, 0—2nd spells (as bard) |
7th |
|
|
|
Whirling frenzy |
8th |
|
|
|
War cry |
9th |
|
Words of Creation |
|
Howling rage |
10th |
|
|
|
|
11th |
Warrior Skald |
|
|
Bardic music |
12th |
|
Song of the Heart |
|
Words of rejuvenation |
13th |
|
|
|
Demoralize |
14th |
|
|
|
|
15th |
|
any |
|
Marcher’s chant |
16th |
|
|
|
Inspire heroism |
17th |
|
|
|
Words of fear |
18th |
|
any |
|
|
19th |
|
|
|
Words of panic |
20th |
|
|
|
Words of fury |
Classes
Harmonic knight is a variant from the Champions of Valor web enhancement for paladins of Milil. It offers BAB and Inspire Courage, and Divine Grace where Charisma should be a secondary score for you (after Dexterity). You’ll need to use a Chaotic-Good-compatible paladin variant (e.g. of liberty).
Warblade from Tome of Battle allows you to take maneuvers, though as you say, not many are very useful to you. Anyway, what you’re really going for is access to the Stone Power and Song of the White Raven feats from the same book; Stone Power is an actually-useful replacement for the Power Attack we need for prerequisites, and Song of the White Raven dramatically improves your inspiration by allowing you to activate it as a swift action. So one maneuver should be from Stone Dragon and another from White Raven. Charging minotaur is a Stone Dragon strike that doesn’t care what weapon you use. You could alternatively take the defensive stonefoot stance, but that leaves you no good options for White Raven. Speaking of, bolstering voice is a defensive stance and leading the charge is a stance that improves allies (but not you since you won’t be charging). Anyway, aside from these, grabbing moment of perfect mind seems worthwhile.
Targeteer from Dragon vol. 310, as pointed out by Matthew M.’s answer, is a strict improvement over exoticist for you. Arrow Swarm is awkward and possibly not worth it, but you’ll have it. Or you could take Vital Aim instead, to get Dex-to-damage on ranged-weapon attack rolls against creatures vulnerable to critical hits. It would also be worth asking your DM about the hit-and-run tactics option from Drow of the Underdark—officially, since both targeteer and hit-and-run tactics want to replace tower shield proficiency, they cannot be combined, but maybe you can work something out. +2 to Initiative is nice, and Dex-to-damage against flat-footed targets within 30 feet is very nice.
Then we get to the prestige classes. Battle howler of Gruumsh from Dragon vol. 311 and warrior skald from Races of Faerûn share the same awful feat prerequisites, and hit a lot of high points for you. You get bardic music, full BAB, some bard spellcasting, and rage, which you can and should swap for whirling frenzy, which is explicitly a variant on rage, rather than a variant option for barbarians. Between Rapid Shot, arrow swarm, and whirling frenzy, you’re entitled to taking a penalty up to −9 for up to four extra attacks. You most likely won’t actually want to do that very often, but between inspire courage and (later) inspire heroism, you will have substantial attack bonuses.
I don’t bother with exotic weapon master from Complete Warrior, though it could easily be swapped in replacing a level of warrior skald. Personally, I don’t consider provoking to be a major problem for archers, since a 5-foot step often takes care of the problem, but YMMV.
Religion and alignment
The religion requirements here actually get a little murky: Milil must be your patron as a paladin, but you “must worship Gruumsh before all other gods.” So Milil likes you for some reason even though you like Gruumsh better. You could, with DM approval, just adapt these classes to a single god, but you could also take this opportunity to come up with a cool backstory to explain why this strange character is the way they are. I’m thinking something like Milil choosing a human born into a human/orc/half-orc tribe that worship Gruumsh to be a champion, and bring those to light. The character might thus be effectively putting Milil to the test, to see if he is actually stronger than Gruumsh, both for him- or herself and for the tribe.
Either way, though, the rules don’t actually object to this. Paladins do not have restrictions on their choice of deity to worship except in Faerûn (which Milil is from), but even there the requirement about putting Gruumsh first does not actually conflict with what Forgotten Realms Campaign Setting has to say about paladin patron deities.
However, if you cannot adapt the classes and the strangeness of the combination is too much for you or your DM, replace harmonic knight below with levels in bard. Your BAB and saves will suffer, but you’ll get better spellcasting and more music. You could even swap a level of targeteer for another level of bard, getting Song of the Heart as a bonus feat per Eberron Campaign Setting’s Music of Creation variant. You must remain Chaotic for battle howler and Good (Exalted, even) for Words of Creation, however.
Feats
As for the order of feats, the first priority is ensuring that you enter battle howler on time, then that you have Dragonfire Inspiration from Dragon Magic, and then that your archery is actually functional. Only after that do we improve your music, first with Song of the White Raven to let you use your first turn each combat, and then with Words of Creation from Book of Exalted Deeds and Song of the Heart from Eberron Campaign Setting to dramatically amp up the bonuses from inspire courage and dragonfire inspiration. Don’t forget to pick up a badge of valor from Magic Item Compendium and cast inspirational boost from Spell Compendium.
Extra Rage from Complete Warrior would be a decent feat to take at some point, since you’ll only get to use whirling frenzy twice per day from battle howler, though there are other options.