steamos? Is that thing live now?
if not, ubuntu probably the easiest
i have linux mint 17 cinnamon on tap but wanted to try and find a distro specifically for gamingHave a look here: http://store.steampowered.com/steamos/buildyourown
would the intel hd 4400 graphics be ok instead of an graphics card?
Not really. I can play HL2 at 2560x1440 with the HD4600. But the graphical settings are nowhere near where they could be with a dedicated card.
There's also a lack of decent games for Linux. Most of Valve's stuff is available on Linux, but if you're hoping to playing much anything else you're going to need to use Wine.
Doesn't bother me though as Valve's stuff is all I really play.
To be honest, distros are pretty much all the same when it comes to gaming. There's very little difference between them. Ubuntu or Mint will let you most easiy upgrade drivers/libraries so in that regard, will be useful, but there's nothing really game-specific about individual distros (although valve claim they've made some performance tweaks with steamos, I've yet to see any benchmarks which show them as being worthwhile).
