First you must ask why you need a generator. If it just to augment the solar a small 1000 or 2000 WATT Honda or Yahama will be fine. My Honda weighs 48 pounds and sits nicely in the gen basket. On the other hand if you plan to dry camp where you will want to run the AC you will need at least a 3000 WATT. Again I would go with Honda or Yahama.
We camped for two weeks last Summer on the Blue Ridge Parkway with little or no sunshine many days. I ran the Honda twice to boost the batteries after several days in a fog bank, but other than that the batteries held up just fine. I have four T 105s.
My only regret is not getting a larger inverter. 3000 Watts would run my AC. Not the standard Dometic. I have an Atwood Air Command that runs on my 2000 Watt Honda.