We use a split-phase 4000 watt generator for extended power outages (which we have about once a year - our house is in a rural area, and the last on the power run, so if the damage is near us we get very low priority - longest outage: 11 days).
The advantage to a small generator like this: It burns less fuel, so we can go a lot longer between runs to the gas station. How do we get by with one so small? Our furnace is a hybrid propane/heat pump. If the heat pump portion won't operate (such as when we're using the generator) it will automatically switch to propane. When on propane the biggest draw is the blower motor. Our water heater is electric, but I replaced the elements in it with 1000 watt elements so that it can be run off the generator. It takes longer to heat, but that's okay. (For normal use, we have an on-demand electric water heater and don't use the elements in the tank heater at all.) The well pump is a 220V pump, thus the need for a split-phase generator. When all of these things are operating they use about 2/3 of the generator's output leaving the other third for normal household stuff. (Obviously these things don't run all the time though.)