catalpa is known in the fisherman's world - the particular moth that use them for breeding grounds leave behind a delicatessen for fish. Most people in southern WV call them catawba worms, and they are a favorite live bait for fish.
Valuable too.
Im mentioning this because if you are looking for catalpa trees and cant find it, then you might ask a fisherman- he may know of some (maybe just ask him for catawba).
As for carving... if you're carving with power than you could use mahogany, cherry, butternut, or it's more famous (and plentiful) cousin black walnut. I have also carved purpleheart, osage orange, and black locust with power. Since they're such hard woods, the features are crisp and turn out great with a high polish.
If you're carving with chisels and a mallet then go with the woods others mentioned already in this thread plus mahogany and walnut added to the list.
As for drying... the paper grocery bag method works well. I get extra paper bags at the grocery store for free. I turn pieces green 1/3 of the way or so, and then put it in the bag and weigh it and mark the weight on the outside of the bag ( what the piece is, the date, and the weight) and store it in my unheated garage. Then I reweigh it every two-three weeks to see how it is drying and mark the weights on the outside of the bag too for a record. I finish turn the result when the weight is basically not changing anymore.
For the impatient and curious- you can also successfully dry new turnings in the microwave. Ive done it and gone from a 6.5" blank of cherry I cut from a stump that day, to finished product that I could bring inside my hvac'd home that night and zero cracking and minimal warping. It takes repeated cycles in the microwave and cooling down. Dont just cook it. This piece was microwaved, and 5 years later zero cracking.
. It took me 45 minutes total of microwave cycles.
Good Luck