I don't recommend to customers that they buy anything less than a 3000 watt if they want to run the A/C. Certain 3000 watt units will power an A/C unit provided the control that reduces engine rpm under light loads is turned off. Those type units cannot react fast enough without tripping when the sudden demand of an A/C compressor occurs. Keeping the rpm's high allow the gennerator to handle that sudden power demand.
A 2000 watt will run smaller stuff OK provided you are wary of cummulative loads of the remaining appliances. Don't expect it to run the refridgerator, water heater, microwave, toaster, hair dryer, tv & coffee maker all at the same time.