What's the difference between a Trade Gun and a Fowler?
That's a good question and one that is a little tricky to answer.
(You can see my answer here:
Smoothbores)
If you are interested in an historic time period or particular style of gun, that will determine which direction you want to go. If you are only interested in killing a turkey, not so much.
I have a Navy Arms percussion double barrel in 12 gauge and a flintlock Chief's Grade Trade Gun in 20 gauge. The 12 gauge will kill a turkey at longer distance but I prefer to use the flintlock 20 gauge. I've never had difficulty calling a gobbler into 20 yards and you can kill them with just about anything at that distance.
For what it's worth, I would say get yourself a double barrel in 10 or 12 gauge then go forth and slay turkey just as effectively as you would with a modern shotgun. Or, if the flintlock bug is calling your name, start researching all the different types of smoothbores available and choose what appeals to you. There is something for every taste and they will all kill turkey.