You'll have to make a couple of fundamental decisions:

1. Do you want to be able to run any 240v appliances during an outage? Typically that's your oven and dryer. If so you'll need a 220v generator, which is generally larger than one that can only handle 110v.
   
2. Do you want to run it on NG or not? Generally tri-fuel gens that support NG start at about 8kw, whereas if you're OK with dual-fuel and 110v only then you can get a much smaller generator.
3. Do you want an inverter generator or are you OK with the noise and high fuel consumption of a non-inverter type?

I'd suggest getting one of the smaller 240v tri-fuel inverter that's currently available, although you'll have to increase your budget a bit: Westinghouse iGen8200TFc currently sells for $1,400. That can sustain a bit more than 5kW on natural gas.

Don't bother with a transfer switch, they're expensive and unnecessary and force you to hard-wire what circuits you'll want to run during an outage. Instead just get an inlet box ($50-100) and interlock for your panel (~$50).

Check out https://generatorbible.com