As
@atanere said, get experienced and pick favorites. Best advice when it comes to Linux distros.
However, off the top of my head... I'd say go for
Lubuntu as it features Openbox and LXDE, both pretty lightweight.
Openbox has been the best window manager for my AMD hardware so far (performance-wise).
Openbox systems always feel (and are actually) snappier when I switch from desktop environments such as unity, cinnamon or even xfce; not that you can't run them on top of Openbox, but they're "naturally" best integrated to the window managers they come with.
You'd save a lot of resources and play some games noticiably more smoothly.
Besides, like any *buntu, Steam OS is Debian-based too, so you get full compatibility if you play Steam games on Lubuntu (all the necessary packages might install mostly automagically from Ubuntu's repos).
Lubuntu+proprietary video drivers should float your goat.
Also, I'd suggest installing xfce4-appfinder, it will help you navigate through your applications (lubuntu only features a xp/w95-like "start menu").