Ryanair did take up the old Buzz flights from STN to SXF. The problem
is, however, that you will arrive at LHR or LGW (most likely LHR), so you will
need something like 3-5 hours to make your connection. That, combined with the
trains across London, will make any price difference moot and be very
inconvinient.
As far as which airport is better, that is a complex issue. For most of
Berlin, and all of West Berlin, TXL is the better airport. It is
Reinekindorf, within the city, while most of SXF (excluding the ends of the runways) is in
the surrounding Bundesland Brandenburg. If you are staying in eastern or
south central Berlin, SXF is a bit closer in and has good connections. If you
are staying in Potsdam, SXF is also a good choice because of Die Bahn's Express
Train.
As far as your connections in the US, where are you leaving from? If you
are making a connection in SFO, I would guess you are somewhere on the west
coast where you might find an airport closer. LH serves LAX more than anywhere
else besides JFK, they also serve PDX, PHX and SEA. Also, if you are near
SAN you can take BA to london and connect to TXL there. I would leave at least
2 hours for your connection, so you can mitigate any possible delays in the
FIS. Lufti always has a transfer baggage desk right outside of the FIS, so they
will take care of it from there