Here's some ideas:
First off, I'd think MPlayer will work fine for you for your video needs. Here's a list of cards that are in the docs from Mplayer's site, and how to get them working:
http://mplayerhq.hu/DOCS/video.html#tv-out
Next for the remote portion. That's also in the DOCS, and might even work for your mp3 streamer as well if you want (since mplayer also plays mp3 files)
http://mplayerhq.hu/DOCS/documentation.html#lirc
And here's a project that is aimed at being ran on a TV, plays video via mplayer, has lirc (remote control) information, plays TV from a TV tuner card, even displays images. It's skinnable, and I think it's a decent idea if you can get it running
http://freevo.sourceforge.net/
Good Luck, and let us know how things go
Cool