A car battery wouldn't last long as it's not a deep discharge battery. I think if the problem was mine I'd go for a cheap Clarke gennie ( about 1kv ) for not much more money than a good leisure battery. This would run a couple of fluorescent tubes and you can also charge batteries from the 12 v outlet
This is all very useful guys, I appreciate it very much. I'm still not sure which route to take! Im going to have to take the plunge and do some trial and error. I like the idea of leisure battery, and a solar charger to help keep it topped up. My get out of jail card is that I'll only need to be in the garage on weekends, so any battery (if I go down that route) I use will have 5 days to top up. That's the theory.