There are many generators I will not name brands other than Honda and Yahama which I recommend
"Contractor Generators" DO NOT take camping.. Period
INVERTER generators.. These are the ones to take with you, They are more expensive but they do not need earplugs to be included.
One special case.. Harbor Freight sells a small inverter job with a 2 stroke engine.. I'm not so sure about this one and would love to hear it under load so I can comment.
Now, how big.
Also there are some small FULLY ENCLOSED generator type generators (Traditional) that are not bad.. I used to have a Genrac 1000
This was a true 1,000 watt generator and it was able to power my Progressive Dynamics 9180 with dead and mean Dead U-2200's hooked to it (Sucking near max power).
2,000 watts will run the Microwvae
3,000 SHOULD run 1 A/C 4.000 will for sure.
Note Im' talking true power. Not peak power.