Judging by what you do on a computer, Linux sounds like it fits you perfectly. The only thing you can't do in Linux is play most PC games.
For getting onto the web, theres many browsers available for linux such as Firefox. You can use xmms to listen to music, you can use mplayer to watch movies. You can use The Gimp to edit photos.
As far as what distro to try, well it depends on your expectations of an operating system. Do you want a distro that will make things as easy as possible, or do you prefer to configure things yourself? If you want a distro that is friendly to beginners I would suggest Ubuntu which is based on Debian. If you are the type of person who prefers to configure things yourself, then I would suggest Slackware, Gentoo, or Debian. SuSE and Fedora Core are also easy for a Linux novice, but they are RPM based. For those who don't know RPM stands for Red Hat Package Management and as the name implies, is a package management system. Other examples of package managers are emerge(Gentoo) and apt-get(Debian). Package managers are used to install programs on Linux systems, alternatively if you don't wish to use a package manger you can compile from source.
Compiling software from source is simple, and can usually be accomplished in three steps:
So to sum it up, if you want ease of use, I suggest Ubuntu, SuSE, or Fedora. If you want to challenge yourself more Slackware, Gentoo, or Debian.
Heres a good site to further research different distros: