You should have no problems with this hardware setup (Hauppauge PVR 150 is a good recommendation)- plenty of power for capturing and playback. Make sure you set your internal hard drive as the record drive.
Capturing standard analog channels from cable should not be a problem, but digital channels or scrambled analog channels are more of a challenge. If you want to capture those you will have to put the output of your Cable-provided set top box into the capture card. At this point you should be able to capture the channels but you will lose the ability to have the card control which channel it is capturing (as this will be driven by the set top box).
If anyone has a work-around to this problem, I'd love to hear it!
Also, most capture cards are standard def. If you want to capture high-def programming you will need to purchase a card that has that capability.
BeyondTV is the closest thing to Tivo from a capabilities and interface perspective, and I think it will only run you about $60. A good deal. mazurek is right on- most software bundled with the capture cards are crap.
If you want to go the free software route there is an open-source project for WinXP machines called Media Portal that I've tried with success - very Tivo-esque.
http://mediaportal.sourceforge.net/
A good link to check out:
http://www.makezine.com/extras/4.html - more than you're looking for here, but a good start.
~Josh