Take it to a reputable shop & replace the tubes with fresh ones to ensure it operates properly, well worth it. They can bias the amp as well.
Dual coil pickups don't buzz like single coils, that's a good idea. Pawn shops are good places to find bargins. The best thing you can do to improve a cheap guitar is put good tuners on it. Cheap tuners never stay in tune. My lead guitarist in my band Money Shot has a Les Paul that has crappy tuners that don't stay in tune. My Les Paul has Grovers on it so it stays in tuner better. Find a guitar that feels good in your hands.
