neat idea, but that turntable doesn't look like it's of all that good of quality. My recommendation is to find a nice used turntable at a yard sale or a second hand stereo shop and use that instead. It does not have any counterbalancing on the tone arm, or any speed / servo control. If you already have a turntable in your stereo, then you are in pretty good shape.
You could also purchase a good quality brand new turntable from a music shop like Sam Ash or Guitar center. NewMark and Technics are the two top-dogs in the turntable industry. Make sure what you use has a good cartridge. Shure and Audio-Technica are my favorites, but there's also Stanton too. The cartridge on that ion turntable looks to be of very poor quality...and that's the most important piece when it comes to getting good quality recordings. Many semi-pro and pro grade turntables come with good cartridge, but make sure what you pick has a standard mount so you can upgrade it in the future if you want to (having a standard mount almost always guarantees a reasonable quality cartridge anyways!). One thing you may also want to look for is an RIAA pre-amp. This will allow you to input directly into any line in on a computer or stereo system. Without this, you will need a pre-amp, or a device with it built in.
Now, once you have a good quality turntable, there are two ways you can go about getting the sound into your computer. If you have a desktop computer YOU ARE ALREADY SET!!! Most desktop computers have a line in ready and waiting for you to plug any line level audio source into. Just go to radio shack, buy a "Y" cable that goes from RCA to mini-plug. Take this cable and plug it into a "tape out" socket on the back of your stereo, and plug the mini plug into the line in on your computer. Next, you will need a recording software. The one I prefer is called "Audacity" and it's an open source program that will make WAV's, MP3's and other audio formats too. It's a very powerful tool that will also allow you to edit and break up the tracks into individual files and such.
Now, if you've got a laptop, or any other PC without a good line in socket, you will need an audio converter box. One of these can be had at any computer or stereo shop for about $50. Again, run a cable between the "record out" on your stereo to your audio converter box and you're set. Now, sometimes you can find audio converter boxes that have the required RIAA pre-amplification built in like this:
http://www.retrothing.com/2005/11/art_usb_micropr.html
You may be interested in this Stanton turntable. It's of better quality, and will give you a bit better fidelity, be less harsh to your records, and is built better. The beauty of this one too is if you currently don't have a turntable for your stereo, this one has an RIAA pre-amp'ed output that you can run directly into it, and use it as a regular turntable when you're not ripping audio files.
http://reviews.cnet.com/turntables/stanton-t-90-usb/4505-7860_7-32417457.html