I have a media PC on every TV now, it seems over time I have upgraded them all to non-integrated graphics and quad cores but your PC doesn't need more than 2 cores (Core 2 Duo or better) and the PCIx graphics helps immensely when playing video, especially Blu-Ray. I suggest any PC and a decent graphics card with HDMI and audio over HDMI. Also if your budget supports it get an SSD boot drive (40g) since the worst part of any HTPC is the boot up time and lag when changing channels etc.
Tuners:
Hauppage (QAM compatible) or Ceton InfiniTV but not both since the seem to clash!
Media storage:
NAS (best solution for multiple HTPC's except when using Ceton)
Non-raid HDD setup, drives get less use since one can be used and other(s) don't have to spin.
Choose a very quiet and cool case, the best are Silverstone IMO, and worth every penny.
Store your PC in a well ventilated place, this helps temps since they will get hot otherwise.
Motherboard:
Most boards come with Realtek NIC cards but they are nowhere near as good as an Intel integrated NIC or external card, helpful when streaming to other PC's.
Memory:
32 bit OS = 4g, 64 bit OS = 8gb recommended.
Windows Media Center and IR remote control will do everything, keep the keyboard hidden when you need it later.
Have fun!