Andy, DO NOT RUSH IN. Sorry to yell that, but I rushed over to the US and got all of my ratings from a prestigious university and was then planning to convert. This was pre-JAA, but in retrospect, non-the-less, it would have been wiser for me to carefully research and find a school that offers both JAA/FAA training and get all the ratings at the same time. There are several just do a google.
Good luck in training.
BBB