People are always quick to post their answers without knowing the question. Is the OP able and willing to do the energy management required to use a marginal generator? Where will the generator be used? If noise is not a big concern, a Champion 3500/4000 watt unit for under $300 will run the AC with no problem, for instance. For all other questions, the answer is, "Honda, or multiple Hondas".
I have owned and operated dozens of generators over the years and cannot simplify the answer to just one brand or model like some of our members do. I don't happen to think a 2200 watt generator is big enough for the application. Regardless of brand.