"-Also, if you are looking to add an IR and CPL on your FAA PPL based on the JAA then you'll need a new valid letter of authenticity (must be less than 6 months old) from the CAA."
Or alternatively, you can just have a full unrestricted FAA certificate issued by doing a skills test with the school you'd be attending. It's a good starting point as they get to see you and, more important, you get to see them. Check it out first though with whoever you're heading to school with.
Think it's already been mentioned, but check out with the TSA regarding foreign nationals and flight training - not sure about the rules for foreigners already green-carded or with residency rights.