When you make your choice, just install mesa-utils until you can find good drivers. NVidia has plenty of drivers for Linux available on their site.
Make sure your distribution has an update-to-date kernel so it's compatible with most hardware.
First you want to know what desktop environment you want to start out with, but note that when you install a distro you aren't stuck with its desktop. I can install Linux Mint with Cinnamon yet still run XFCE anytime I wanted.
Prepare for a lot of screenshots.
KDE, this desktop is pretty and comes with a few neat effects out of the box. Not quite recommended if you have a bad graphics card:
The distribution in this screenshot is Kubuntu, the name should be self-explanatory.
XFCE, this desktop is minimal and classical. No amazing graphics out of the box but can be achieved with things like Compiz. This is an incredibly lite experience:
This is Xubuntu. The name should as well be self-explanatory.
LXDE, this desktop is incredibly
lite. Absolutely perfect if you have low RAM:
This is Lubuntu.
Unity, most people don't like this desktop including me in some ways, but I would recommend it for any new user:
This is simply Ubuntu.
Here is my favorite. I f**king love this desktop. It's called MATE, it's based off of Gnome 2.0. Amazing:
This is probably the most customizable one, in my opinion. Not certain what distro is in this screenshot.
And last, but not least, Cinnamon. This is the default with Linux Mint:
I shouldn't even have to say what distro this is.