what the FAA requires
It seems that I remember something about the regs stating you must have an oil pressure gauge and, I think, a compass, but as far as other instruments there are things you would like and things required. A GPS is not required but might be nice to have. You don't even need a radio or a transponder if you do not plan on flying into controlled airspace. I am sure someone more knowledgeable than me will chime in here. Good Luck.