I personally prefer Xubuntu (= Ubuntu + xfce) since xfce is the most light-weight desktop environment available for Ubuntu. For mining it shouldn't make a difference though. Just make sure to get the latest stable Ubuntu version with the latest GPU drivers. Especially drivers can make a huge difference in performance.

You can always go for other Linux distros, but in my opinion Ubuntu is the easiest one to set up for a beginner and I'm not aware of any mining-specific distros.