Don't bother with a JAA PPL. To start the ATPL ground studies, you only need an ICAO PPL, doesnt have to be CAA.
Find a good, reputable FAA school and do the stand alone FAA PPL. It's cheaper, includes a night rating and IMO will give you better handling skills. From someone that has done both FAA/CAA PPL and CPL, the FAA skill tests were much more practical and your knowledge is really tested during the oral portion of the check ride.
You'll find many people that disgaree with going the 'American route' have never flown in the states.
Never pay up front, let any one threaten you with cancelling your visa and remember you're the customer!