Welcome to LQ!
It depends a great deal on why you want to use Linux. If it's for your work, then the Linux distributions you usually meet there are Red Hat Enterprise Linux, SUSE Enterprise Linux, and Debian Stable. The first two cost money (if someone gives you a DVD of either, then it's only a demo) but there are similar free ones.
Red Hat: the official free version is CentOS. For home use you need extra software, which is available, but not yet for version 7, so get version 6.
SUSE: this is based on OpenSUSE, which is free and suitable for home use.
Debian Stable: this is free, but there's a very nice modification called BOSS produced by the Indian government, which I can recommend.
Fedora I'd avoid. There's nothing wrong with it (Red Hat is based on it) but each version is only supported for a year and it's where new ideas usually show up first. Often they're good ideas, which eventually become standard, but the Fedora users sometimes get to try them when they're not quite ready.
Go to http://distrowatch.com/
where you can find notes about the distros I've mentioned, with links to reviews where you can find out more. There are also short reviews here, of course.