Flyah,
It is best to check the exact requirements with your training provider as I know it can vary from place to place - different interpretations of the same rules...........
I can tell you that I have required TSA approval for every training event I have had in the US (FAA and JAA alike) but have never required a visa (UK Passport holder).
Some friends of mine have trained at other schools and been required to get M1 or B1/B2 visas variously, so it seems a bit hit and miss really.
As I say though, best bet is check what your training provider wants you to have and go with that.
I've just completed my latest TSA approval yesterday ready for some fun in the sim in a couple of weeks time and the process seems to be running smoothly at the moment
Enjoy the States when you get there too.