Testing generator output

If you already own the generator I say go for it and try it out. If the generator is anywhere decent then it will regulate the voltage more than enough for a motor so you won't over power the motor with voltage. If the generator can't handle it you will not harm the motor unless you are able to stall it for an extended period of time; the generator shouldn't be harmed either it would be like trying to use a dead battery if it can't push out enough juice it just won't.

The reason I've notice that people suggest higher wattage ones is because they are typically built a little better and since they are capable of more wattage they respond to a peak significantly better, I'm going into peak discussion. Generators supply electricity on demand (even the power stations'), a household generator will produce approximately a few hundred watts at idle, as more items are plugged in/turned on demand rises and the generator senses it and runs harder. Since there isn't a preemptive notice about this, the generator will typically spike/peak higher than the demand and recovery back around what it needs to put out. A motor turning on with capacitors will typically be able to handle that lag, the capacitors will just charge up slower (almost not noticeable in most cases) and the capacitors work as rectifiers handling another other voltage changes during operation. Motors without capacitors also typically handle it but since they don't get a beginning zap from the capacitors you run a small chance of burning out your coils, imagine plugging a 220v motor under load to 110v source it will energize the coils but remain stalled.

If this is a more permanent installation (off grid scenario as opposed to hurricane prep, etc.) I recommend a separate motor starter kit - bad with naming here - before the motor or a heavy duty UPS/Battery system but for just when the power fails I think you'll be fine.

I would not recommend a square-wave/modified-square-wave generator to run your furnace. The control boards in them are particularly sensitive to high-frequency noise induced in those sort of designs. One particular failure mode is that non-sine inputs cause excessive heating in inductive components, whether they be AC motors or current-filtering inductors on the control board.

Looking around, it seems that gas furnaces should be provisioned for 350W, and about the same for a typical refrigerator. 700 watts of steady-state load isn't bad, and I would argue that a 2000W steady-state pure-sine generator could handle the transient loads from start-up currents no problem, leaving plenty of room for laptops (75W - 100W), cell phone chargers (~10W), and lights.

Go with the pure-sine wave.