I actually wouldn't recommend Fedora for a Linux newbie, I'd recommend Ubuntu or Linux Mint. Simply put, with Fedora it requires a little more of a "hands on" approach to install JRiver Media Center and to update it (has to be updated manually since there's no Fedora repository). Fortunately there's a Fedora script for installing JRiver Media Center which makes it much easier, but like I said updating is manual, as in you have to manually run the script again when there's JRiver Media Center updates. With Ubuntu and Linux Mint you just add the JRiver Media Center repository of your choice (latest, stable and beta) and install and update Media Center from your distro's package manager (e.g. Synaptic).
Using Ubuntu or Linux Mint with JRiver's repository is the easiest, most straightforward way to get Media Center installed on Linux. If you had some Linux experience, then Fedora would be a great choice if you can handle the more "hands on" approach to installing and updating.