As rough numbers go, I agree with George.
If you are going down to the the 2kw range, I'd recommend that you beg/borrow/ rent something close to what you are considering, and test it first.
Some of the newer furnaces can get finicky about the supplied power - they can be quick to pull the trigger and deem a voltage dip at blower start-up as a brown-out, and shut down. YMMV.
I bought a 2kw in '98 during our big Ice Storm, and loaned it to my sister. Ran her old-school basic gas furnace just fine. Still have that gen, and it runs well.
Recently, I bought a 7kw Briggs, as I need to support a furnace/well pump/sump pump at minimum. I like that gen, and it's good value for the money. But loud (knew that before buying), so an add-on car muffler is on my project list....
Money no object Home Support: I'd go with a Nat Gas fired automatic start/transfer system at home, no question.
Money no object Portable: Inverter class generator. They provide very clean power, and can provide better watt/per/watt startup performance. First stop Honda, maybe Yamaha.
By that I mean a 3500 watt inverter class generator may handle short-term brown out load conditions better than a a conventional 3500 watt gas generator. As in the furnace example I cited.
The other nice thing with many of the inverter class gens is that they can be easily (1 patch cable) synchronized/paralleled. I'd really like the flexibility of having 2 x 3500 watt generators that can be used separately, but readily paired up to generate 7kw when needed.
The other nice thing with the larger portable generators is electric start is often standard. I find my 7kw fairly easy to pull start, but for some people the electric-start is a Must Have. With a larger gen, make sure it has a good wheel kit.
One source to consider is a well respected local equipment rental. Many of them will rotate their equipment fleet fairly often - if you can put up with a few scratches and dings, you can get a used gen (that probably has seen better than average maintenance) at a good deal.
Rgds, D.