Talk to a TPWD official before taking any fish home. Keep it nice and legal so you don't end up paying fines or having to destroy your fish. Don't take any forum-goer's word for what is or isn't legal in Texas.
Texas has several catfish species. A few, such as the headwater and Chihuahua catfish and the two blindcat species, are very rare and should not be taken, but you probably won't come across those anyways. Otherwise, which ones you can keep depends on how big a tank you can provide.
Flatheads, blues, and channels all get enormous and need a much bigger tank than a typical home aquarist can provide. They do well in ponds, though.
Black and yellow bullheads get to about 20" and will do fine in a tank with at least a 24" X 48" footprint.
Freckled and tadpole madtoms are the smallest Texas catfish. They are usually less than 5" in length and can be kept in a ten gallon aquarium.
This page should help with ID:
http://www.bio.txstate.edu/~tbonner/txfishes/. Scroll down to Ictaluridae for native Texas cats and Loricariidae for introduced armored cats.
What are you calling perch? There are a lot of fish that go by that name.