How much experience do you have with Linux? If you're new to it, Damn Small Linux might be a little confusing... really, though, Linux isn't that heavy, if you can get a little extra RAM it should easily handle just about any distro, it really comes down to preference. Ubuntu and Mint are considered the most newb-friendly ones around.
Ubuntu 8.04 ran fine with 256MB RAM when I last tried it, I don't know how much the requirements have gone up, but I think you should be alright.