Haggis,
Being self sponsored is a very good reason indeed why you absolutely should care where you train. I'm sure there can be no worse feeling than returning to the UK only to discover you have been short chamged and now have to self-sponsor your retraining or additional training.
I have no experience of any of the schools in California so can't comment on them specifically. I started my own PPL training at a school in Stuart, Florida many years ago called Treasure Coast Flight Academy, nice glossy brochures, instuctors all in gold bars and run by a complete ass. I learned a lot about about schools who promise PPLs in 4 weeks, never mind those who now promise it in 3.
I finished off at a much smaller outfit, Airwise Aviation in Titusville, Florida which was great. That was back in the early 90s but I believe the owner Gary Evans now runs a school in Merritt Island, Florida. I don't know whether he does JAA or not, or just FAA.
It could be worth doing the FAA licence and then converting. That's what I did although the conversion procedure may be more complicated now, I haven't checked for a while.