Are you only getting the FAA private in the States?I`d strongly advise you to go for the "whole package" with commercial/instrument/multi, as well as flight instructor, that is if you`re planning of making a career out of it.
It is my understanding that you can fly G registered aircraft with an FAA certificate, but only with PPL priveliges.But to be sure you should contact the UK CAA and ask about foreign license/certificate validations.This seems to be the norm throughout Europe with regards to the individual countries` CAAs.
If`ve you`re only planning on getting the private, then I`d say do it all in the UK so that you won`t get caught up in the validation beaurocracy.
The visa deal is more up to the flight school than yourself.Once they`ve given you the OK to enroll in a course, they`ll send you the papers/forms which you in turn bring to your local US embassy.There will be some days` waiting to get it approved (don`t know how bad it is nowadays) but this is normally not a big issue.
Don`t have any info about the SA scene, but Orlando FT seems to be OK - at least that`s what I`ve heard.Get in touch with some of their students and instructors to get the "reality facts" in stead of the "advertisement facts".