Basically it's a normal PC, but as quiet as possible. So choose a motherboard that's passive. On-board graphics card, or seperate card that's passive. Quiet PSU. As few hard drives as possible. IR Receiver and remote. You'll want to choose a cool running CPU. Looking at 2ghz PC as a minimum.
XP with a front end will be sufficient (Meedio, Media Portal) or could use XP MCE, or perhaps Linux. You'll want a soundcard with ASIO drivers if you plan to sent audio to a AV amp.
Software wise Power DVD, FFDSHOW, Real Alternative should be enough.
Can't help with recording from TV though, guess need a TV tuner/DVB card.
IMO I would buy a MATX 939 Mobo, use your 3700 for the HTPC, buy a faster one/dual core 939 CPU for your Gigabyte system.