Just graduated to a travel trailer after a few years off. Started out with a tent then had a couple of pop-ups so never too complicated an abode. I'm wondering what everyone has in their basic too...
Since you RV is a "house" on wheels, get an apartment or house orientated basic tool kit. It will have things like picture hangers, anchors, etc. We have one and it has turned out to be more useful than the expensive, professional tools in the basement.