There are many, many, many different ways to do this, depending on how fancy you want to get.
The simplest, IMO, is to get an old laptop with an SVGA-out, a newer laptop with HDMI-out, or put together a small desktop with a TV-out (RCA, SVGA, DVI, HDMI, whichever) capable videocard.
Configure it to boot into whatever GUI you are most comfortable with. Make it work with the TV-out so you can use the TV as the monitor. Connect up a wireless keyboard/mouse or even just a remote that can act as a mouse. Set the default font size to something big so it's legible on the TV.
Then just share a directory off your server (NFS, Samba, however you want), mount it on the media box, and use whatever video player you want (Kaffeine, Codeine, Dragon Player, MPlayer, VLC, Totem, etc). I do this using FreeBSD/ZFS/NFS on the backend, and an old laptop running Kubuntu 8.10 using Kaffeine on the frontend.
Or, you can go all the way and use something like MythTV, Boxee, or any of the other media server solutions.