Ideally you want a genset that will put-out about twice what your load will be. This gives you some elbow room to handle startup surges and future growth. Ideally you would tailor the genset to your particular loads, but usually it doesn't work-out that way in practice. Most people will buy what they can afford and then re-engineer the loads to match available power.
I can tell you from experience that a Honda EU2000i will run a small microwave on the playa without issue. It will also run any toaster you can throw at it. But it won't do both at once. There is some reserve power available when you are toasting, but the microwave will take most of what the EU2000 puts out at the density altitudes found on the playa. As far as charging batteries, this will not tax it at all. It is a rare battery bank indeed that can safely handle more than a couple of hundred watts of charging power.
FWIW, generators vary radically in how quickly they derate. I like the Honda's because they don't suffer from the extreme derating that some the cheap gensets do. Basically you get what you pay for. I have seen a new 5KW B&S throw-away struggle to start a 12000 btu AC on the playa, whereas a 3K Honda did it nicely. The Honda put out nearly the nameplate sea level watts even though it was facing the same 7500 foot density altitude conditions as the Briggs. In the end it's all about conservative design and how much surplus torque the engine can produce compared to the generator end (or inverter) rating.
If you want to get nerdy, a good density altitude calculator is here: http://wahiduddin.net/calc/calc_hp_dp.htm
It can be used to derate quality engines, but it will not accurately predict the effects on a throwaway-type engine.