I’ve never heard of that Showshifter program, but why pay for it when you can get programs that do the same thing for free?
VirtualDub is a great freeware program that has all the advertised features of Showshifter and a whole lot more. You can edit video and even install free filters that denoise, blur logos, and all kinds of other effects. See the capture guides at http://www.vcdhelp.com for more information.
As far as TV cards go, any cheap one should do. The Hauppauge WinTV line has some good cards. It’ll probably cost you between $40 and $100, depending on what features you want. There are some that cost several hundred dollars, but only because they include things like expensive bundled video editing software, which you won’t need.
If you only plan to watch the shows once and are unconcerned about quality, you can capture straight to Divx or MPEG. This will make ugly, blocky-looking videos because the computer is compressing on the fly. Due to the large amount of processor time the compression takes, your video may also be prone to dropped frames. It’s best to not even attempt this option if your computer is slower than 1GHz.
Alternatively, you can capture to RGB, YUY2, or a semi-lossless codec like HuffyUV. These options will make HUGE files (30-50 GB/hour) which you must then convert to a Divx or MPEG. Unfortunately, even my Athlon XP 1800 isn’t fast enough to view the huge HuffyUV files directly without skipping.
The conversion is a time-consuming process; it takes me about an hour and a half to encode a 30 minute show on my computer. However, this produces much better quality in the end and is the method recommended by just about everyone.
A final option would be to buy a hardware encoder that can produce somewhat comparable results to software encoding, only in realtime. I mentioned this last because it’s probably out of your price range. Hardware encoders usually run anywhere from $600 to $15,000, sometimes even more.