You do not wanna be using the beta Winamp on GNU/Linux. There's a great alternative called XMMS. Most distros should include it. Its a clone of Winamp with codecs to play almost any audio filetype. If ur looking for an iTunes-like media player then there's Rhythmbox. There are countless media players for GNU/Linux but these are among the more prominent ones. For video there are Xine and Mplayer. Google these. Most distros should include a few good media players so u shouldn't really worry bout that.
For a distribution, I would recommend Fedora Core 3. In my opinion its pretty good as its not too "noob". You actually don't need to use the terminal to install software as well. There's this program called APT. Just download the APT RPM from www.rpmfind.net
for ur distribution and type
apt-get install (package name)
and it'll solve all the dependencies and install the package. There's a GUI for it called synaptic as well.