Since it appears that some ACs won't run on the 2000, which is the one I plan to get, do you know which 5000 btu unit the guy was using?
What you want to do, if at this time you do NOT have an AC unit, is find out how much start up watts it needs, along with the how many watts it needs to run. The start up watts is usually what kills a gen set/ AC combo. The AC may run on say 1800 watts, but it needs 2200 to start the thing up, which kills the genset. Or in your case, do not buy a 2000 wt unit, get a 2500 or higher unit since you have neither at this time.
Then also look at watts needed, if you want to charge the batteries WITH the AC on, then you would need using my above figures. the 2200 to start the ac, or get the AC going at 1800, then hook up the charger that may need say 1200. Now you need a 3000wt genset.
It is pretty simple in some senses to figure out how big a genset you need, others, you get screwed up by forgetting things like start up watts, and only look at running watts!
Hence when I bought a genset for my RV trailer back in 92, I bought a 3500 wt version. I could, and still do run most of my house when it was not in use with the RV. It is WAY to big to put on my boat, but, things to think about none the less.