Your going to get 95% of people come in here and shout ubuntu, ubuntu, ubuntu. I'm not going to say anything as I think it's wrong.
What I will say is YOU AND ONLY YOU can decide what distribution to run. As your the one who has to use it, I really think you should try as many linux distro's you feel like. As you are clearly a beginner and have stated you want nothing more than for "it just works" I strongly recommend downloading the following distro's, and in same cases variants of distro's and make your own mind up:
http://www.ubuntu.com/desktop/get-ubuntu/download
http://fedoraproject.org/
http://linuxmint.com/
http://www.opensuse.org/en/
http://www.pclinuxos.com/
http://www2.mandriva.com/pl/
Now this is where things get interesting:
Lets take the OpenSuSe distro, it is a linux OS but you get things called Desktop Environment's and they can look like:
This one is OpenSuSe with the Gnome desktop:
This one is also OpenSuSe but with the KDE desktop:
There are a lot more desktop environments but I would look at them two for now.