You have got to get your FAA licence sorted first, no FAA licence = no airplane rental! It is not as simple and straightforward as it used to be and the paperwork from the CAA to the FAA doesn't take a day or two either! You may have left it too late already! What you may need to do is to fly your hours with an instructor. Flying the S.F. Bay area is somewhat more complex than a bumble around the British countryside and the chances are that you are going to need a few hours of instructor time to get up to speed with flying in US airspace anyway.
"Private renters insurance" may be a good idea. Rental insurance provided "free" by the FBO's in the US is at best basic and at worst, completely inadequate. You may end up with the bill for all or part of any damage to the airplane. Also, your holiday medical insurance will probably not cover you for mishaps whilst flying so you will need proper travel medical insurance specifically for flying. Bills in the USA are always HUGE. Try Traffords 0844 815 0970 you will need this whether you are flying P1 or supervised.
Good luck!