Coming up with the right hardware definitely is half the issue. Building one of these systems from cast-off hardware probably will be less than satisfying.
The CPU probably will be used mainly for encoding and decoding video, particularly if you are interested in high-definition TV. If you have hardware encoders for this, a lot of the work is taken off the main CPU, but if you are using software encoders, you can expect to need about 1GHz of processing power (whatever that means these days) for every stream of video.
Hardware encoders, such as the Hauppauge PVR series, unload quite a bit of CPU utilization and allow a single CPU to encode multiple streams at once. This would be useful if you wanted to record one program while watching another or record two programs at one time. On my system, it recognized my Hauppauge PVR-150 with no problems.
If you are building the system yourself, be sure to study the LinuxMCE Project's documentation and the pages of MythTV's documentation that discuss hardware.