Personally, I would not reccomend any of those cheap USB tables though. The sound quality is terrible and they are hard on your records.
The alternative is to to use one of the better turntables made for true high-fidelity. I would suggest tables made by VPI or Rega. I also personally like the Technics SL-1200. The problem is any of these tables require a little more investment, and they will also need a phono preamp. The output can be run into the audio inputs on a PC for recording to CD. But once you've chosen this route, you may find you prefer to listen to them directly.
A third alternative is sort of in-between. There are some USB tables with magnetic cartridges that look like they may suffice. They aren't going to be as good as the high-end tables, but the magnetic cartridge will help improve sound quality. Here are a few: