What is a good generator for my house?

My house has hot water baseboard heaters fed by an oil fired furnace which also supplies domestic hot water. At 120VAC its maximum startup current is 6.5A and normal running current is 2.3A. This is just 780 watts startup and 276 watts running. Toss in a few light bulbs and a 1kW generator will still be adequate.

First of all you need to calculate maximum load which must be delivered. Measure the power requirements of your furnace and any other devices you plan to use. It sounds like you don't want to install a transfer panel. That means everything must be plugged in with extension cords, eliminating the practical use of anything that requires 240VAC.

I suspect your furnace will be the single largest load. A 2500 watt generator will likely suffice and give added capacity for television, or even a microwave or toaster oven.

I use a 5500 watt generator which connects to a transfer panel to power much of my home.

You have to figure out what the wattage requirements are for all the items that you want the generator to run. Add 25% for the items that you forgot about or your wife decided she wanted. Then select a generator that is that or above. You can also get a whole house generator from Home Depot and have it installed so that it automatically comes on when the power fails. They can run on natural or LP gas.