It depends on your battery draw. During the summer in higher elevations, I could go for a week just off a single battery. Nothing in my camper uses battery unless I turn it on. The Norcold 300 doesn't use any battery in LP mode either. Since I don't have a TV or radio, my only draw is the fan and lights, which are minimally used.
My recommendation would be to add a good battery monitor such as a
Trimetric 2025. This will allow you to figure out your battery consumption which is needed to decide on how much capacity you need.
Just adding batteries or solar without knowing your consumption is like putting the cart before the horse. And just running a generator is almost as bad since you don't really know if you need to run it or not.
For hooking up your generator, just get a
plug adapter and plug the camper into the generator. Recommend at least the Honda 2000 so you have enough power at higher elevations.