Most of the veteran muzzleloaders use Blackhorn 209. It is considered the premium powder, even boasts more power and higher velocity, but the big thing is that its so much cleaner. You can fire upto 20 shots without ever passing a cleaning rid through it, which also means less corrosion, or nore.
As far as bullets the more experienced hunters use Barnes 250 grn TMZ, expensive but will mushroom and kill at most any velocity, which means extended shots will kill.
They also use CCI magnum primers. This is highly recommended for Blackhorn 209. I use them also even though I am still shooting Pyrodex powder, at least till its goe, got 5 lbs left.
If you haven't gotten a scope yet then I and many others highly recommend the Nikon 3x9-40 BDC. Its an excellant scope, possibly the best, and ultra clear. It has the bullet drop compensating reticle, which helps for longer shots.
Good luck, I love my Omega. Oh, one more thing. If you fell the Barnes bullets are too expensive, then try Hornaday HPXTP 300 grn. They are also considered a premium muzzleloader bullet although much less expensive. Use Harvestor crush rib sabbots and will load decently, but maybe with some effort, which you can expect with a Thompson as they have a premium tight bore.
by the way, most of the guys here are CVA fans.