Running an AA battery charger takes a tiny amount of juice. The combination that is cheapest and easiest is an amorphous solar (PV) panel tied to a lead-acid battery. The battery can simply be the one in your car, riding lawn mower, or even the UPS for your computer.

You could probably squeak by with a 5-watt panel if you have lots of direct sun, but you can get a 15-watt panel for nearly the same price. And often, you can find great deals on 45 or 60 watt amorphous panels ganged together at retailers like Costco etc. These often include a charge controller so you don't fry your battery. Note that amorphous panels are relatively large and heavy for their output - fine for home and car camping, but not for backpacking.

I would strongly suggest getting a basic multimeter if you're doing anything with solar panels. These can be had for under 10 bucks, and they will let you confirm polarity and check the voltage of your main battery (esp. important if you don't have a charge controller).

There are smaller and more efficient solar panels out there, but before you buy keep in mind that there are some big technological improvements in the pipe that should drop the cost per watt way down. So buy only what you need now, and save your shekels for the next wave of photovoltaics.