Q: If you do buy a cheap car to play with, what are you planning on doing with it?
Consider this: my commuter car provides me with quite a bit of entertainment repairing little things that were neglected by the previous owner and gives me peace of mind when I drive it into SF and leave it there overnight. Sure, some punk might break into the Honda (it has happened twice the month) or some dumbass might back into the bumper but hey - it's the commuter car!
You may have other needs and that should drive your choice in a second car. Examples: track rat, winter car (if they salt your roads), off-roader, dune buggy, drag strip terror, etc. Hell, if you have the cash, perhaps you can buy a kit car (Lotus Seven, Cobra replica, etc.) and the requisite donor vehicle (Mustang 5.0).
While a moped is a great idea to learn how to fix something inexpensively, IMO if you don't live in an urban/campus area where you'll use the thing regularily, it'll just be an expensive toy. Also, if you never drive it, nothing will ever break so you won't have anything to fix
Just my 2 cents.
-g
One last thought: If you are looking for a cheap car that will ALWAYS have something to fix, how about an old VW Beetle Coupe/Convertible? It may not be your style but a friend of mine bought one years ago for $600 and it provided him countless hours of repair time. EVERYTHING is user servicable and quite simplistic but the downside is that you'll always find something to fix. Hell, I remember helping him rebuild the engine on his dining room table - twice.