I ran a setup as you described in a shed many years ago. I ran it off a brand new truck battery and had a large solar panel on the roof. It worked okay but was a bit limited, as the lights would go out suddenly as the battery drained. You'd probably be better off buying a brand new truck battery which will give you the amp hours that you will require, as old car batteries will probably not hold a charge for long enough. You will probably need some heavy duty solar panels and a controller to prevent your batteries getting cooked in very sunny weather in summer. Generally you need heavy, thick wire for anything on the battery side, but on the other side of the controller you will only need light wires to run things like lights. Best advice would be to visit your local solar power shop and they will be able to fit you up with what you need and calculate things like charge times and amp hours. Back when I did this solar stuff was fairly cheap, but could be expensive these days. I'm not sure as I have not done anything with solar for like 15 years. Might be an idea to shop around a bit. Good luck with your project.