Obligatory doofus legal disclaimer: I am not a licensed electrician. You should use a licensed electrician to install anything electric in your home. And this is not legal advice!
You can power most of a small home with a 7-10kW portable generator. I think 10kW or maybe 12kW is the largest size you can get in portable form factors. The things you will run into trouble running are heat/AC, water heater (tank-style, tankless should be fine to run), well pump (no worries if you don't have well water), dryer, and electric range. You may be able to run one of those alone. More on selecting loads later. When choosing a generator, you'll need to sit down and calculate what loads are critical. The sum of those load's max power requirements should be used for choosing what wattage class you're in. Some generators are dual fuel, meaning you can use gasoline or propane.
There are a few ways to get power to the things you need to run:
The easy way is to run a 120V drop cord (of the appropriate wire size for the loads you'll be running) from the generator to the inside of your house. Plug the things you want to run into the cord and you're good to go. You wont be able to run any hard wired things or 240V stuff like A/C&heat, dryer, well pump, etc.
The best way is to get power to your main panel. You must isolate your generator from the main electrical service to your home. This is crucial and legally required so that you don't backfeed electricity into the grid (those transformers that step transmission line voltage to 240V work backwards, too!) and put line workers at further risk for electrocution. Furthermore, you run the risk of damage to your home's electrical systems and devices when the main power comes back on. Bottom line here is that the main breaker to your house must be OFF before you feed any power to your house from the generator. There are a few right ways to get power to the main breaker, and almost all of them require the services of a licensed electrician. Your choices really boil down to an automatic transfer switch, a manual transfer switch, or a panel interlock configuration. An automatic transfer switch does all of this automatically. A manual transfer switch sends power to loads that you manually select when power is lost. A panel interlock works when you have a way to feed power to a breaker inside of your main panel from the generator. The interlock won't allow you to transfer power from the generator to your home's loads unless the main breaker is off. From there, you can select which loads to power by toggling the individual breakers on/off inside of your panel.
There's a lot I left out. Post up any questions y'all have.
