Well, pump and pressure tank installed in 2018, 500 ft uphill from house. Separate grid service to well, with professional installed transfer switch with 4-prong connector for generator. In panel, 2x100 amp fuse from grid switching to 2x30 amp fuse; well pump connected via 2x20 amp fuse; 4 GFI receptacles connected via one 20 amp fuse. Pump is Flowise model 10 gpm, 1.0 HP, 230v (do not know motor manufacturer). Pump is at 145 ft depth and static water level is 24 ft. Would be nice but not necessary to power the GFI receptacles also.
Realistically the smallest generator you can find that has a 240v receptacle is usually rated around 3500w.
For an actual calculation the nameplate rating for the pump would be nice, but it's probably submerged. A typical Franklin 1 hp pump draws about 5A @240v, you need a minimum of 50% overhead for startup, that gets you to 1800w, plus whatever accessories you need in the pump house.
I have heard people having difficulties using cheap inverter style generators with motors, they seem to be too sensitive for inrush. The inrush on a motor under load given an ideal source can easily be 5x the rating during the first couple seconds. I think the solid state circuitry of an inverter has to be protected with less tolerance than a wound rotor generator.
The purpose of using 240V is to reduce the voltage drop over the 500+145' wiring length. Normally you associate 240V with high-power loads like a water heater, but that's not the case here.
However, generators that small are generally only 120V. Unless you're going to do something fancy with a transformer, you'll be forced up into a 3000W+ generator simply to get 240V.
But we can do a bit better
First, my pet peeve is houses that are completely broken without mains power. That is unnecessary.
On this water supply, your magic word is "uphill". People don't say that for 2% grades, so at 500' I'm guessing we have at least a 30 foot elevation difference, and my guess is, a fair bit more.
30 PSI water pressure is considered fine for a city house (but you can get by with less). You get 1 PSI for every 2 feet of elevation difference. If you have a big tank at the top of a hill, your water system will passively pressurize all by itself from gravity.
All you need to do is keep the tank topped up every few days or weeks, depending on your tank size vs your usage. A 500 gallon tank, in my household, means spinning up the pump every 5 days if we ignored the power being out; we could stretch it to 20 days if we really had to. If you want a 10,000 gallon tank, those are available too.
Go look at Pure Living For Life's early videos on their homestead build; they go deep into their hilltop tank system. They are amateurs and bumble through it quite sloppily and make a lot of mistakes (that system is overkill), but that's the gist. (At the time they were going for wholly off-grid; they couldn't make the solar work due to inexperience so they finally got grid power. But in an outage, they will have water for a month.)
The rest of the house
"Ah, but my furnace needs power". Not to make heat; merely to push the heat around. One or two well-placed Empire style wall furnaces can take care of that passively with convection. Further, they can be configured to run off a Nest when power is available and off a millivolt thermostat when power is not.
The refrigerator needs power too, but that is within the reach of a modestly sized battery system, which can be replenished either from a generator or solar. That battery system can also handle basic lighting and entertainment.
You use any generator, possibly a borrowed one, to top water tanks and batteries.