Disclaimer: I haven't used either distro. Having said that, I think DSL is rather a dead project, the successor is Tiny Core. I don't have any experience with either but if I were faced with your situation, I think I'd opt for Tiny Core.
1. Minimum System Requirements
Wired Internet Connection
USB Memory Stick, also known as a USB Pen Drive with a known filename on it; this will help you to identify your stick.