A 3,500W unit will power a 10,000 BTU AC unit and a little extra. If you want to run more or around the clock you need to consider that. I have a 6,800w/8,500w surge Home Depot special. I'll run one of my 2.5 ton AC units at the house, 2 frigs, TV, a few lights without issue. If you're ust running the AC unit a Honda 2000 or the like would likely work but those aren't budget conscious gensets.
Its sounds like you might want to consider that $699 unit from Harbor Freight. I already have a couple Hondas but I'd look at them hard if I was shopping.