Congrats on the new gun!
I think before you get new bbls, consider getting the action worked on and get the trigger pull you want for hunting/shooting.
To answer your question though, what do you hunt?
T/C makes a bbl for everything that walks/flys.
I live in an area that limits deer hunting to ML and shotgun; no centerfire rifles.
I want to get the ML pistol bbl for my Encore, I think that would be a hoot, but the .375JDJ is the cartridge for medium to large sized game animals; the handgun equavalent of the 375 H&H. If you learn to master that, you won't need any other cartridge for deer, bear, elk, hog, etc.
You might want something for the smaller furbearers like grounghog, coyote, fox, etc...
.223, .204 Ruger, 22-250
Any way congrats and good luck!