There are really only a few things to power. Most of the time a generator that supplies 20-30 amps at 120V should be enough.
Growing up in the rural midwest that's exactly what my father had setup. He had a 20 amp Honda that had a special breaker panel that would plug into it. It had 3 circuits on it, the furnace, the well pump (we didn't have city water) and the refrigerator. When the power went out he would go and throw those breakers in the main panel, and connect the generator in the garage, and plumb it's exhaust out the special port he had built there, so that he could keep it inside out of the whether. For all cooking/lighting we turned to fossil fuels of some sort, whether oil lamps (of which we had many antiques that we would put to use) or a propane camp stove for cooking.
If you have FiOS or something like that, make sure you power your ONT, otherwise powering the router may be a crap shoot, as if it depends on the cable system it may or may not stay up, and the same thing with the phone company, if the DSL will work, then your regular old POTS would still work, so no point in powering up a router and VOIP just to emulate the already powered POTS.
If you are looking into a full house system you definitely want to go with something diesel, probably Kohler, where for small 20-30 amp generators, Honda gasoline models are hard to beat.