A ha, now I get it. I thought you already a video capture device. For under $100, you're going to be looking at something with a software encoder, in other words, the processor in your computer will have to do all the work of capturing and compressing the video.
I'll have to defer to other folks on this. The last time I used a software solution, I wasn't very happy with the results.
If you don't have a speedy processor, I'd consider a hardware solution like the Hauppauge WinTV-PVR-USB2. It will cost a little more, but it's works great.
I think this is also hardware encoding,
http://www.plextor.com/english/products/TV402U.htm, but it will not work with vista or mediacenter.
I don't think any of these will serve as audio outputs, so I'm not sure how realistic it is to expect double duty in REW.
Anyone else have options to consider?