Its good to see you are thinking of utilising visas the best way possible. I would advise getting an M1 visa to begin with for the majority of your training, get most of the JAA school work done and get your FAA private license done either before or during your JAA training. Then when you are ready to get your FAA commercial, go and get the J1 visa, as you cant get a J1 after you have your FAA commercial license, so they say! then you will only have a few months left of school, and you get your CFI and instrument and have at least 18 months visa working time, to get some good hour building.
Good luck with it all. Let me know if you need any help with info on the visas or the school.