Converting LP to digital. Advice please...

I've been thinking of creating a library of lps on my computer. So its not that easy it seems. I thought i could use my unused preamp RCA output to my mic in on my lap top? Would this work using Audacity software?

I use an old way.
I use a CD Recorder (Marantz DR-700) connected to a preamp (Rogue Magnum 99). It records up to 80 minutes of audio into CD audio format. Then I store them on my computer in mp3 format. You can use either CD-R or CD-RW.
No extra software is required.
The sound quality is at least as good as CD if LPs are in good condition. The only catch is that, if the LPs used are noisy, the Marantz recorder does not recognize the end of of each tracks. Then, you need to manually stop and start the recording for each track.

Thanks for all the help and advice. I was wondering since I have a CD recorder if I could record onto a CD-RW. Then take the CD-RW and transfer it to my computer and is there a software that will let me add the individual tracks and then transfer it back to a standard CD? Sounds like a lot or processing but maybe the cheapest way of doing this.
If not then I need to look at some of the other suggestions here more in depth.

I connected my amp to my PC using the tape input to the sound card line in. Then I use Roxio 10 ($50) to record each side as a .wav file. I use Click Repair ($40) to remove clicks and pops. Then I go back to Roxio 10 to edit, separate out the tracks, name the tracks and burn to CD. It is time consuming but the results are pretty good. If you want to hear the difference I will e-mail you a before and after.

Alan do you feel that the Click repair does so by narrowing the bandwidth? I just wonder how it identifies the clicks and pops if not by frequency. I would be interested how that affects the final sound.