Hey Steve, first off I'm sorry to hear of your loss but the outdoors will do you well.
As far as the generator goes, it sounds like your camping style doesn't require much electricity which puts you in the market for maybe a 1000 or 2000 Watt generator. That should be plenty of power for what you need.
Two major things to consider;
1) I would recommend a QUIET power generator thus you would want to look at inverter generators. It makes a world of difference when you are out in the wilderness.
2) If you plan on charging your trailer battery with the inverter generator I would strongly recommend purchasing a proper 12v battery charger and running it off the AC outlet of your inverter generator as opposed to charging the battery DIRECTLY off the generator. This is because generators typically do not have a shut off sensor when the battery is fully charged and you risk overcharging and thus damaging the battery.
I found this site to be really helpful when it came to finding the right inverter generator for my needs;
https://www.quietpowergenerators.com/generators-vs-inverters/The "inverters vs generators" page is very insightful and arms you with the knowledge necessary to make an educated purchase. They also have detailed reviews of the latest and best selling inverter generators on the market.
Hope this helps Steve. Safe travels!