3000 watt likely will do what you want, but may be heavier than you want to handle.
A 2000W inverter generator is likely to have problems starting the AC unit, especially at higher altitude. But it will be quite and easy to carry around. Add a micro air easy start to the AC and the 2000/2200W generator will likely do what you want.
Now quiet & cheap are somewhat mutually exclusive. PLEASE do NOT buy an open frame cheap generator. Spend some money on a quiet inverter generator. honda yamaha and champion have some nice decent quality quiet generators in the 2000-3000W range.
We boondock a lot, have a 13,500 BTU AC unit, an 1000W microwave and have a single honda 2200 W generator. My brother has the same. The AC units have the micro air easy start installed. Both of us consistently run the AC units at altitude approaching 7000ft with zip problems starting or running the AC. That said a honda 2000, or yamaha 2000 will eventually (20 minutes or so) overload at altitude above about 4500ft.
Just can't run the AC AND microwave at the same time, but a 3000W wouldn't let you run both at the same time either.
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