Hi LH2,
The fuel price difference is negligible between LF and LS, and LF are usually much better value landing fee wise.
Annemasse and Annecy are both great GA airfields on the edge of the alps. If you want LS in the log then Geneva is cool, but arse at weekends until the end of the ski season (as is Chambery), and most of the nearby fields are domestic only.
IMHO Annecy is the best option.