Make sure you use a charge controller, and as suggested try to stick with 12v (add a car lighter socket) rather than using an inverter.
For starters a car battery , 10w panel and 5amp charge cotroller is fine. If you continue down the solar route you may want to consider a deep cycle battery, better controller, fuses and also add a small inverter for other uses.
Once you have a small set up, I'm sure you'll get hooked.