I recco the name brand saws, Stihl, Husky/Jonsereds, Dolmar above all
others for normal wood-cutting, but in your case, check out the
electric saws. Look for power tool name brands, Makita, Dewalt,
Craftsman, etc.
The problems with 2-cycle engines usually start (they don't start?)
when they're left sitting too long with old gas in the tank and carb.
Running the saw dry and draining the fuel each time is a real pain,
often forgotten.
Electric is the way to go there.

JohnK