Generator size for well pump
Realistically the smallest generator you can find that has a 240v receptacle is usually rated around 3500w. 

For an actual calculation the nameplate rating for the pump would be nice, but it's probably submerged. A typical Franklin 1 hp pump draws about 5A @240v, you need a minimum of 50% overhead for startup, that gets you to 1800w, plus whatever accessories you need in the pump house.

I have heard people having difficulties using cheap inverter style generators with motors, they seem to be too sensitive for inrush. The inrush on a motor under load given an ideal source can easily be 5x the rating during the first couple seconds. I think the solid state circuitry of an inverter has to be protected with less tolerance than a wound rotor generator.