I would suggest one of those Renogy modules mounted to a lightweight stand and a cheap controller to start. You might consider replacing the battery you're using as it sounds like it has been abused and won't have the greatest service for your style of camping. A good replacement solution would be two Costco or Sam's Club 6V GC2 batteries. The price is close to one good 12V deep cycle battery and the 2 X 6V solution is a proven winner.
Good luck with your solar charging. If done right, there's no more need for a generator.