Ubuntu is by far the easiest 'out of the box' distro to run and will automatically identify and install drivers for even some pretty obscure hardware like unusual keyboards with extra buttons/volume controls/whatever.

I can't say I'd recommend Fedora for gaming -- it's certainly not been a priority for Red Hat as they've been pursuing the enterprise market -- but there isn't any reason you couldn't run linux games on any distro you wanted.

If you're more interested in performance, something like gentoo is a good blend of optimization and ease of use.

All that said, you may well find that whatever distro you like best is the one to go with. I've experimented with several different distros and have a couple I like (debian and gentoo), but it really comes down to personal preference.

Addendum

Another thing that you may find problematic is driver support. new hardware -- especially notebook hardware -- can be poorly supported initially. It may take a while for good drivers (depending on manufacturers as some are better than others)

Also, while the distro you choose can make a big difference, the desktop environment will also be significant. The two big ones are KDE and Gnome, but personally I prefer some of the leaner window managers. Again, it's a personal choice, but if you don't like what you try initially, you can always change it.

Don't forget to check out http://www.phoronix.com for good benchmarks of Linux distros.

You are a fps gamer? Then forget about Linux for couple of years. Now there is very limited amount of good shooters under Linux. I agree that Ubuntu is best right now. You can't play BattleField2 (wich is already old game) and newer games on Linux.

PS: Linux is not only for servers, it just not for games currently. But again, it is still possible to find cool games that suit you, just more harder than in Windows.