I run my house off of my Onan 2.5 kW gen. in my camper. You just have to be careful not to overload it or it will trip the breaker. I run a #12 extension cord from the microwave outlet in the camper to my transfer switch in the garage. I use the microwave outlet because it is a 20 amp circuit and because it is not GFCI protected. Since my home's transfer switch only switches the hot wires and not the neutral (like any other home transfer switch) it would trip the camper GFCI outlet if I tried to use one of those.
I have added a transformer to make 240v AC for the well pump. A 3 kVA transformer is large enough for my 3/4 HP pump. I paid about $300 for it at an electrical supply house. You can also get an autotransformer from Outback Power, the X-240. It comes in it's own enclosure with a breaker.
My well draws about 2 kW running. I'm not sure what the starting surge is but the gen. handles it. I have fluorescent lighting in almost the whole house so that draw is quite low. If I turn on every light in the house it's only about 2 kW.
