AFAIK, there is no such thing as a Linux-based "Mono OS". You'll probably need to modify an existing distro.
Since you claim not to be a Linux expert, Ubuntu might be a good choice, but it's a bit of a heavyweight. You'd need to spend a lot of time disabling features to trim it down, which requires quite a bit of Linux knowledge, so it doesn't really help you avoid learning Linux. Same applies to Fedora, SuSE, etc. If you intend to develop on a platform that closely resembles your target platform, keep in mind that these are arguably "nicer" distros for daily use than the ones I'm about to suggest.
Something like Gentoo gives you a lot of customizability, and works on lots of hardware (possibly a plus if you plan to put your media center on exotic hardware).
Easier to use, but still lightweight, is Arch Linux, which would be my personal preference for a project such as this. It's very lightweight, and relatively easy to use. You still need to be comfortable with command-line, config files, man pages etc., but it's better than Gentoo or LFS. The only isssue I can see is that it's 686-optimized, so it might not fit your hardware.