I have two, which I got as "good used". A light-duty 2500 that's portable. Good to run the refrigerator and small stuff around the house or out and about around the ranch. A 5KW which would run a whole house, including conventional A/C. I don't really need that much, given my propane cookstove and water heater.
The capacitor-start load of a refrigerator is some 20 amps; running, it draws around 8. So, you need 20 x 120, roughly, for a minimum size if you want to run your refrigerator in the usual fashion. A 2500-watt, then. Now, it won't hurt things to have your TV and/or computer on; a momentary flicker at startup is all.
The longest outage we've had here is some 40 hours. Normally, no more than two to four hours. If night time, I don't really worry; just go to bed early. Daytime in summer, I mostly just run the evaporative cooler and a light or two plus either the TV or the computer. (Yeah, I know; evap coolers don't work in Alabama.
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For a good standby unit, I'd figure on intermittent use. Daytime, give it a rest every tankful of gasoline or thereabouts. If you don't open the refrigerator regularly, it only needs to run about an hour or so every six to eight hours. In hot summer, kill out the breakers for unnecessary stuff so you can have the A/C.
Overall? Add up the amps for "gotta have" loads. I use 60-watt light bulbs; I call them one amp just for conseratism's sake. Amps times 120 or 240 = watts. If you don't run full load on your generator, it'll do fine for constant use.
I'm not impressed by the mufflers they come with, though. A 5KW will quite possibly annoy the neighbors.
Don't leave any fuel in the tank during non-use. Test it with a minimal amount of gas in the tank and then run it dry. If you can easily disconnect the fuel line to the carburetor, give it a brief shot of WD 40 and crank the engine a bit before storage. If you really want it ready and fueled, use StaBil.
If the carb cruds up from sittiing, spray carb cleaner through the fuel line is a Good Thing. Check and write down stuff like the number of turns of the idle mixture screw from "runs good" to "closed". That way you can pull it and spray carb cleaner in the hole. Same for any other sort of adjustment screw. No magic to it.
Read the directions.
Make sure they're in a "keeper" place.
Art