Most any will give you the freedom to do stuff like that. All the Linux distros are escentially the same. Same general programs, same hardware support etc (of course newer releases have newer stuff).
You have the commonly use RPM-based distros:
Suse, Fedora/Redhat, Mandrake.
They all descend from the same original Redhat OS from a few years back and are mostly the same and try to stay similar to each other. Mandrake is usually considured the most newb friendly version out there, but I prefer Fedora because of it's official support of
yum and apt which makes keeping up to date and installing programs much easier.
Then there are other popular distros that are packaged different from the rpm-types and are individualistic. Gentoo, Debian, Slackware.
These tend to be used by more advanced users, but Gentoo is probably now the most newb friendly out of this bunch. Commonly used by people who just want the latest and the greatest it has a very involved installation proccess that can be very intimidating. It has very good support forums and decent docs to make up about it. The biggest downside is that it's source based distro, which means that you download the programming source code of the applications and compile them as you install, which can take a very long time. Upwards of 2 days on even a fast computer. People say they learn a lot from it, though. And there are binary packages aviable that speed the installation proccess up by quite a bit. It concentrates on performance and customizability.
Slackware is a no-frills type deal which concentrates on simply providing basic functionality that a knowledgable user can modify and extend apon. This distro is a great crash-course setup for people that don't want to be hand-held and want to learn stuff quickly. But it can be very frustrating.
My favorite is Debian, which is what I use for my desktop. It's claim to fame is the apt-get package tool and it's very high quality, and very very numerious packages aviable for it. Tend to be very confusing for people new from Windows.
Just pick a distro and try it out. Maybe Fedora if you want. They just released a new version that you can mess around with. If you don't like it then just try out a different one.
edit: Oh, I forgot about knoppix. Knoppix is a Debian based Os that runs directly from a cdrom. Called a live linux cd. That way you can try out Linux on your computer without having to install anything on your computer.
you can find many links to iso image downloads at
http://www.linuxiso.org/
Also check out the home websites of the distro your interested in. A quick google search will turn up lots of stuff.
also check out
http://distrowatch.com/ to check out some of the not-so-commonly used versions.