The RV Ready Champion 3500watt generators are the best bang for your buck that will meet all your needs (Micro, Air, charge) and the expense of noise/size/weight. This is the route I initially went. Hauling the generator was fine as long as I had my ATV trailer however when I went camping without ATVs (without trailer) it wasn't reasonable to bring the Champion 3500watt. I also didn't like to use the Champion 3500watt when camping in the vicinity of other campers.
As time went on the wife became less interested in ATVing and more interested in relaxing and comfort. As a result I purchased a Yamaha 2400watt inverter based generator. This works fine, it is easier to move around and much quieter than the Champion. Let me repeat, more mobile and quieter! This combination works great powering AC and Microwave (I assume not both at the same time).
All this said, if I were to do it again today, I would probably go with a 2000watt inverter based generator for even easier mobility. If the Champion 2000watt would power my AC I would go with that. Otherwise Yamaha or Honda 2000.
With consideration to your budget and my experience, I would recommend trying to determine if the Champion 2000watt inverter based generator would power your AC.