Lots of good advice on here. Couple of things to add . . . .
Send of your paperwork and money to the CAA straight away. They can sometimes take a little while to confirm your existence to the FAA.
Then send off your paperwork to the FAA (they don't need any money!). Specify a FSDO where you can conveniently present yourself to the FAA and be placed in receipt of your temporary FAA licence.
You need to do a BFR with an instructor before you use your licence out there. No big deal, although it wouldn't do any harm to familiarise yourself with the way the airspace out there works before you go. It's all a bit different.
You will love flying out there! Cheap aircraft rental, almost no landing fees, 24 hour airports etc.
Need to know any more PM me.
Have fun!
Julian