I think most people would recommend Ubuntu if you're new to Linux. Have a peak
here.
There are some caveats, however. Depending on the video card you're using, it may (or may not) be fairly straightforward to install kernel drivers for it. ATI cards tend to be a bit more difficult to get working (although I understand that's been improving--slightly). Ubuntu is fairly straightforward, though, so installing these drivers should be little more than just clicking a few buttons. You'll probably be prompted at some point after installation about "non-open" drivers or some such, then it'll give you a list. Just download them.
Now... there are a few caveats that you'll want to keep in mind. Ubuntu CANNOT distribute certain codecs, decoders, and libraries because they're legal status is unknown (or theoretically illegal) in the US. Specifically, these involve: MP3 playback (although you don't have to install anything to get them working, AFAIK, since most media players have their own built-in decoders; Fedora doesn't let you, though), DVD playback (you need decss if you plan on playing region-encoded or copy-protected DVDs, and decss is technically illegal in the US), and any related WMA/WMV/MP4/AAC media formats. Usually, in these latter cases, you can simply press forward through a few dialogs and eventually get the right things installed. It's a bit of a pain, but blame our legal system, the DMCA, our copyright law, and Congress. They're the idiots that have made this such a mess that anyone without the express blessing of the content industry cannot write their own software to play back things
they own.
Oh, and Ubuntu makes installing eye candy pretty easy. You'll probably need to update a few packages after you install (it'll prompt you) and then go to System -> Preferences -> Appearance -> Visual Effects (tab) and you can enable compiz-fusion from here.
Disclaimer: I don't use Ubuntu regularly nor do I use Gnome as my desktop environment, which is what Ubuntu comes with by default. I use KDE, but Kubuntu (Ubuntu with the KDE desktop environment) doesn't play nice with compiz-fusion.
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Once you decide to take the plunge, go ahead and make another post. I can point you in the general direction of some things you might want to learn. But be aware that it's largely going to be a pretty significant learning experience and you make impact head-on into the learning curve. Expect to find some activities to be reasonably easy to perform but expect a few others to be quite difficult. While Ubuntu is much more polished for the desktop than other distributions it's still a bit sharp around the edges. Expect to get cut.