I have been doing a lot of studying of the subject since I suffered through a week at Sun'n'Fun in 2014 at 90F+ and the 2500W inverter/generator would not start my AC.
Flipflop is right, even if you have a soft start device so a 2KW gen can start the AC, it will be at 90% of capacity (my AC pulls 1440W running) and you are not supposed to run over 80% long term. So you need something rated at least at 1800W continuous
just for the AC.. Fagedabout charging the batteries, running the microwave, or even a TV/laptop.
So last year my choice was a Westinghouse WH2400i (2400W/2100W). NP starting the AC and I also had 200W of solar plus a 1KW inverter to make my coffee (770W) while the AC was on.
The key is figuring out an energy budget to determine what you need and want and then identifying sources.
OK that was last year and if you wanted clean power to run "sensitive" electronics (laptops, tvs, charge cell phones) you needed an inverter generator and most advertised <3% THD (measure of how "clean" the power is, particularly important for COPD devices) and non-inverter generators (mainly open frame "contractor" devices - drills don't care) were running mostly 10-20%THD. That had been true since the first Honda inverter/generators at the end of the last century. Unfortunately they are still selling those same designs (and frankly my EU2000i bought in 2009 gave me more trouble than any of the others I had. The good part is there is a lot on the web about how to disassemble, clean, and reassemble the carb.).
This year is different. The manufacturers have realized there is a big market for clean (enough) power for RVs that can run the AC and a number of inexpensive single stage (no inverter) 3KW-4KW class devices that are "RV ready" (have a 30A TT-30 plug and <5% THD which is "enough" for everything I have tried).
Pro: 3KW is enough for everything you want to do including running the AC (starts my 15,100 btuh with barely a grunt and no soft start) & are inexpensive (one I bought was $349.95 on Amazon)
Con: 17" is too wide for my rear compartment (2400 stores nicely), are heavy - 80 to 100 lbs (but have wheels which make them 4" wider), and thirsty (four gallon tank needed to run 12 hours)
Also the best ones are quiet, under 64DB, and have CARB, EPA, and Forest Service approval.
For more than you ever wanted to know, see my
series of web pages on the subject. Keep in mind that this is evolution in progress and what we have today was not though possible (or very expensive) in 2014.
One thing I really do not understand is why the generator manufactures do not seem to have a clue how to market to the RV industry.