i have a Home Worx DVR but it only records OTA HD signals, not cable hdmi or component video from a cable or Sat box
for recording in HD , from digital cable, their DVR box is the simplest and easiest
if you don't mine recording analog SD signal, you can buy a tivo etc. style DVR
HDMI signals are copy protected, it part of the requirements of mfg
there is no "inexpensive" equipment (that i know of) that will accept and record an HDMI output from a cable or Sat box
you did not specify if you wanted to record std 4:3 definition video
or full screen 16:9 HD video