Any of the mainstream ones will work for steam and desktop use and are generally very stable. I'm not going to go into the techincals of each distro because each one works very nicely and has a ton of packages and utilities to customize it. I personally love Ubuntu. Version 13.04 is very stable and fast. The problem is that not everybody likes the "Unity" interface that Ubuntu has. If you haven't heard of it, here's a quick video:
https://www.youtube.com/watch?v=fAcdFd0MmH0
Linux Mint is also very nice. The newer version of it include the "Cinnamon" interface. It's a more traditional interface and behaves similar to windows 7 in my opinion (task bar, launcher bottom left, windows in middle, tray bottom right). Here is a screenshot I found:
http://4.bp.blogspot.com/-a4o8ksXLnkI/T70TWM0Gi2I/AAAAAAAAI_k/RNwYiAJkifQ/s1600/linux-mint-13-cinnamon.png
Cinnamon also has a "Mate" interface which is basically the old gnome 2.x interface. I personally wouldn't use it but if you like the traditional gnome feel you might like it.
I don't have much experience with Fedora but I have always heard good things about it. I think the default interface is gnome shell. I personally don't mind gnome shell but I wouldn't recommend it to anyone else.
So to conclude: All of the mainstream distros are superb. Ubuntu is my favorite, but you might not like their unity interface. Linux mint is amazing and does everything Ubuntu does but uses a Cinnamon interface which is very nice. I'd go for either Ubuntu 13.04 or Linux Mint 15.
Note: I kept using the word "interface" but the correct word is actually
Desktop Environment (shortened to DE).