Good info, GaryBy, Thanks!
Also FWIW, I'd check the amp draw & voltage drop when that well pump starts, as too low a voltage could damage something in the house (some motors will overheat), and too much of a draw could hurt the genny - but if you're not tripping a breaker it may not be too much current. If they're on different breakers on the genny you could draw too much without tripping any breaker. Don't forget that as voltage drops, some electrics will draw more current to obtain/maintain constant power, which only makes it worse.
I had borrowed a 5K Coleman once during a power failure here and it ran my well and furnace OK, but I never checked them at the same time the refrigerator was running. That's why I'm looking for something just a bit bigger, those 3 are the necessities, anything else is a luxury. When I first powered the house up with it - after 28 hours with no power - I shut down the breaker for the furnace and well. Once the refrigerator was up and running and the sump pump finished, I powered on the well, waited till the well pump shut down and finally put on the furnace. Furnace last because I knew there would be an oil burner and 3 circ pumps running at once - the other 2 were used later.
My recollection is that the boiler (oil burner + 2 circulating pumps) didn't seem to cause as much as a dip as the microwave, and certainly not the refrigerator. Since we weren't running the generator 24 hours, the refrigerator really wanted to be running whenever it had power. After a couple of days of just adapting to life without external power, I wound up toggling things at the transfer panel to reduce the chance of problems. Fortunately, our well pump usage is fairly predictable.
Now if only we had had the deep freeze right after the ice storm. Then I could have emptied the freezer and stored it all outside.