Zero Binder Levels
Stupidly, anima mage does not require levels in binder at all. The Bind Vestige and Improved Bind Vestige feats are sufficient to meet the binding prerequisite:
Special: Ability to bind a 2nd-level vestige
That’s all there is to it, and Improved Bind Vestige says this:
Benefit: When you bind a vestige using the Bind Vestige feat, you do so as though you were a 5th-level binder. Thus, you have access to vestiges up to 3rd level, though you still can bind only one at a time and gain only one power from it.
Worse, the sloppy wording of the anima mage’s Soul Binding class feature means that if you have no levels in binder, anima mage levels “stack” with your zero levels, so that you make pacts as a binder of the same level as your anima mage level would.
Soul Binding Bonus: At each anima mage level, your soul binding ability improves as if you had also gained a level in the binder class. Your anima mage levels and binder levels stack for the purpose of determining your bonus on binding checks, the effectiveness of your vestige-granted abilities, your ability to bind higher-level vestiges, and the number of vestiges you can bind. You do not, however, gain any other benefit a binder would have gained.
Nothing in there says anything about “existing” binder levels or levels in a binding class you had before taking the prestige class. It even literally says that your soul binding ability improves “as if you had gained a level in the binder class.” Someone with Bind Vestige and Improved Bind Vestige can take a level of binder, and they get the binding of, surprise, a 1st-level binder (and lose the ability to use your Bind Vestige and Improved Bind Vestige feats). Anima mage is saying you get that.
Compare the very next section, on the anima mage’s spellcasting:
Spellcasting: At each anima mage level, you gain new spells per day and an increase in caster level (and spells known, if applicable) as if you had also gained a level in an arcane spellcasting class to which you belonged before adding the prestige class level.
So, for example, a wizard 3rd/anima mage 3rd casts spells as a 6th-level wizard and binds vestiges as a 3rd-level binder.
It goes without saying that doing this makes the two feats worthless, except for avoiding binder levels. There are plenty of builds that would gladly spend a level to save two feats, but wizards or other full-casters probably aren’t among them.
Effective Character Level: cannot be 1st
You can never take anima mage as your first level character level because prestige class prerequisites must be met the level before you take the class, and you’d never get the spellcasting requirements without class levels anyway.
Plus prestige classes are defined as a special type of multiclassing, so arguably you simply cannot be a single-classed member of a prestige class. See this answer for a more thorough discussion of a single-classed prestige class character; most of it applies here as well. (Technically, the cheese proposed there could work here, too, using feats to build up magic to qualify for the arcane spellcasting requirements of anima mage, but that feels beyond the scope of this answer. Even if you did it, anima mage would have no spellcasting to progress and it would be pointless.)
Minimum-level entry: ECL 2nd
It is possible to enter anima mage at second level in a campaign that is using the flaws variant (Unearthed Arcana). You need four feats: any metamagic feat, Bind Vestige (Tome of Magic), Improved Bind Vestige (ibid.), and Precocious Apprentice (Complete Arcane, page 181, not with the rest of the feats). To get all four feats at 1st, you need to be human and take 2 flaws.
Bind Vestige has no requirements, and Improved Bind Vestige only requires Bind Vestige. Plenty of metamagic feats with no requirements exist as well. So those three cause no problems.
Precocious Apprentice can only be taken at 1st—no problem for us—and requires “arcane caster level 1st” and “spellcasting ability (Int or Cha) 15,” which are easy enough for all arcane spellcasting classes except hexblade (Complete Warrior). Dragonfire adept (Dragon Magic), shadowcaster (Tome of Magic) and warlock (Complete Arcane) arguably qualify as well, though that’s stretching things a bit: they all have an “arcane caster level,” but it’s not clear if having Int or Cha 15 works for the “spellcasting ability” requirement since they don’t cast spells, per se.
There are also skill requirements to worry about: 4 ranks each of Intimidate and Knowledge (the planes). Strictly speaking, the level-up rules have you choose skills before feats or gain class features, so you have to be a class that gets both of these as class skills; you cannot rely on a feat to give them to you if you want 4 ranks at 1st level.
For many others (who have Knowledge (the planes) but not Intimidate), there is a way to get Intimidate in-class for free: be either of the Lion Clan from Rokugan (Oriental Adventures; note that the 3.5e update for Oriental Adventures in Dragon vol. 318 eliminates the rule restricting humans to an ancestor feat for their bonus feat), or from the nation of Kozakura on the continent of Kara-Tur in the Forgotten Realms (Dragon vol. 315).
Enchanter wizards alternatively have the option of taking the social proficiency variant from Unearthed Arcana. As a variant class, the social proficiency enchanter gets Intimidate in-class natively, not as a separate class feature.
Finally, sorcerers with the blood of Siberys variant (Dragon vol. 351) get Knowledge (the planes) as a class skill. Importantly, Oriental Adventures is quite emphatic that you are free to use its mechanical material in other settings, ignoring the lore as you like if you want, and likewise Eberron has “everything in D&D has a place in Eberron” as a core setting tenet, so combining the Lion Clan’s Intimidate with the blood of Siberys’s Knowledge (the planes) should be possible.
The classes that can achieve ECL 1st qualification for anima mage, allowing one’s first anima mage level to happen at ECL 2nd, are:
- Requiring nothing more than the feats themselves:
- bard (Player’s Handbook)
- beguiler (Complete Arcane)
- death master (Dragon Compendium)
- dragonfire adept* (Dragon Magic)
- shadowcaster* (Tome of Magic)
- warlock* (Complete Arcane)
- With the feats and the social proficiency variant (Unearthed Arcana)
- enchanter wizard (Player’s Handbook)
- With the feats and either Lion Clan from Rokugan (Oriental Adventures) or from Kozakura, Kara-Tur, Forgotten Realms (Dragon vol. 315)
- duskblade (Player’s Handbook II)
- sha’ir (Dragon Compendium)
- wizard (Player’s Handbook)
- wu jen (Complete Arcane)
- With the feats, and Lion Clan/Kozakura, and the blood of Siberys variant (Dragon vol. 351)
- sorcerer (Player’s Handbook)
* assuming they were ruled to qualify for Precocious Apprentice
Without Knowledge (the planes): minimum ECL 3rd
While it’s possible to get Intimidate in-class no matter your class, I can find no similar option for Knowledge (the planes). Sorcerers have the specific blood of Siberys option, but most other classes do not have so many options.
Without a way to get Knowledge (the planes) in-class, you’ll need another class level, making anima mage 1st happen at ECL 3rd. Of course, this means you’re some-kind-of-spellcaster 1st/something-else 1st/anima mage 1st, which hurts your spellcasting, and the obvious “something-else” here is binder (since that way you can save a feat by taking Improved Binding instead of Bind Vestige and Improved Bind Vestige), at which point you’re just talking about regular entry to the class.
If you don’t want to multiclass and lose spellcasting, you’ll probably won’t get the skill ranks until 4th or 5th, because you’ll need a feat to get more class skills, and you don’t get one until 3rd, and then you need to put skill ranks in that skill on the level after that because of the ordering of the level-up process. At that point, it’s probably better to just go ahead and wait until your cross-class maximum becomes 4 at 5th level.
But if you really want, you could use shenanigans to get more bonus feats. Worshiping an elder evil, moderate or severe taint, etc. are ways to get more feats. Do one at 1st, and you can get your skills at 2nd and start anima mage at 3rd. These have some serious drawbacks, and even so are usually banned for being too cheesy, but then, on that note...
I strongly recommend all DMs ban this, however
With a single binder level and the Improved Binding feat, you qualify for anima mage and actually have the Soul Binding class feature to progress. This is far more balanced and appropriate, so I strongly recommend that DMs require that single-level dip.
Preventing Improved Binding from working, and requiring three levels of binder, is going too far. That makes anima mage a huge self-nerf that doesn’t seem appropriate.
Banning Precocious Apprentice and other early-entry spellcasting tricks is also strongly advised.
So the result is prepared-caster 3rd/binder 1st/anima mage 1st or spontaneous-caster 4th/binder 1st/anima mage 1st. So I suggest that you consider ECL 5th the first level you could take as anima mage as a sorcerer.