I'm in a similar situation to you, so I'll just add the little that I know.
Composite bows + footpads
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Composite bows are non armour piercing (I think), so if you play against ulm, for example, they won't do much damage in the first 3 rounds, and then afterwards they'll hurt your footmen more than the enemy
.Since you have imperial crossbows, that isn't a problem.
Ordinary/Imperial archers
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Ordinary ones are much cheaper, so normally better. Except, of course, if you end up in an archery duel with heavily armed archers. They are also much, much worse if the enemy gets through or round (or over) your front ranks
Cavalry
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Against your standard enemy forces, no cavarly is just fine. However, so types of army are succeptibly much weaker without a flanking cover (something on your flanks to protect you from enemy flanking attacks). You cant always rely on melee infantry to do this as they'll most likely head for the center scrap, leaving their position empty. However, the horse archers are relatively good for this, as they'll stay where they are (since they're firing their bows) and they'll put up a good fight if attacked.
Heavy cavalry
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Even if you're planning on a defensive tactic, it's worth having a few heavies on 'attack rear', occasionally they'll go straight to the enemy commanders and finish the battle before it started
Enemy fliers
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Early on they're quite rare, though a few draconians or devils on 'hold and attack archers' will mess up your nice plans
Celestials
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I don't know much about them. The pigs didn't seem to add any tactical element, and my other computer foes were already vanquished by the time I had enough crystals to conjure anything else
