Ok, I am not an expert by any means...in fact I am a wannabe like yourself. BUT, speaking from experience do the JAA licences.
I went to the USA and did my PPL there, got an FAA PPL as I had originally planned on getting all my FAA licences and working out there. Since returning I have completely changed my mind. The JAA licences are much harder to convert to from an FAA licence than converting from a JAA to an FAA later. I plan on doing this myself eventually.
Even my FAA PPL has restricted me, as I cannot get my night or IMC ratings here until I have 100hrs and do some exams to convert my licence to a JAA PPL....its all very fustrating!!!
If I were you, I would do all your licences here with the JAA, then later when you are in the USA convert to FAA...it would be a hell of alot easier!!
Hope this helps.