What size generator to run AC??

Don’t know brands to buy, but do know that while you CAN get by with a 2200, a 3500 range will provide sufficient power and allow more things to be run without issues.

Champion 3400 has remote electric start.

Champion 2500 dual fuel will run a 15k even on propane, what it won't do is run that and anything else but lights and tv. Your fridge would need to be on propane (with a 12V compressor fridge you'd need solar and to turn off your converter) and no microwave or other big appliances like a coffee maker. You can step up to a 3400/3500/3600 watt unit to alleviate those limits but you pay in weight, cost, and fuel consumption (both max and min burn rates).

I agree with the MicroAir but with the 2200 you won't have much left for anything else. I like the Honda 3500 but if money is an issue many are saying good things about the Predator 3500.

A 3500 watt should handle it. If you get a soft start for your AC, you can power a 15K BTU AC with a Honda 2200 invertor. It actually works out cheaper to spend $300 on a Micro Air Easy Start and save $1000 to get the smaller generator (assuming you buy the big name brand).