Each class of generic characters (the ones you can create) has six tiers. The first tier is unlocked when you unlock the class. To unlock later tiers, you must have a character of that class (doesn't matter which tier, but you only start with the first) at at least a certain level. For example, to unlock the fourth tier, you may need a character of any of the previous tiers at level 200.

Higher tier characters have higher stats, weapon proficiency (weapon experience gain rate), and usually aptitudes. The increase is strictly incremental. Also, it also requires more mana to create or trangsmigrate into higher tiers.

Transmigrating is where you re-make a character as another of either the same class/tier or different class/tier. The character will become level 1 again, but there are benefits; it would probably just sound like a dumb idea if you're new to it, but it's mostly for post-game, not advancing through the story, although you may do whatever you want. Here is a good place to read about it.

Yes, the warrior could be more powerful than a battler, but a battler would have more potential (assuming a battler is a higher tier than warrior, I don't remember). Transmigration becomes an option whenever you have the Mana, but it takes a long time to regain the levels lost while still through the story, so I suggest waiting until 'later'.