Harbor Freight's Predator generator is the most generator for the cheapest price. However, they carry only a 90 day warranty and you will not find any repair shop that will work on one or even repair parts available. Therefore, consider them disposable.
Champion generators have a solid reputation with a support network of repair facilities and available parts. They are very favorably priced, and probably the best bang for your buck.
Honda and Yamaha are premium generators with a price to match. Either would probably last a lifetime, but pricewise do not deliver a value.
The previous suggestion of buying two inverter generators in the 2000 watt range and tieing them together when needed to run the A/C is a good one. That way, you can use just one generator if needed, but two when the extra wattage is required. Also the two generators delivers managable weight, and you can purchase one a time making it easier on the budget.