There is more than one way to go.
I use a hybrid inverter/charger which is rated for 3000 watts. It has a load support feature which allows me to supplement the generator power if the supply is insufficient to my needs. That means I can run the roof air, microwave, coffee pot, toaster, and fridge all at the same time.
The load support also allows me full functionality when plugged into a 15 amp shore power supply, without blowing the shore power breaker.
In your case I'd get a 4000 watt hybrid inverter/charger and mate it with a 3500 watt Champion inverter generator. That generator comes with remote electric start--so for small loads, or short duration loads the hybrid inverter/charger can be used.