Converting LP to digital. Advice please...

If you have serious $$$ invested in your TT playback rig and are transcribing priceless software, you might want to consider the Korg MR-1000 DSD recorder ($900 street price).
This pup records DSD to internal hard-drive and can record several ways to CD.

I use the Wadia 17 AD converter from the tape out of my Ayre K1x preamp then digital via Yamamura Millenium XLR digital to an Alesis Masterlink recorder. You can split each album side into their individual tracks and then create a CD from it. The sound is fantastic.

I use an M-audio Delta 1010 AD converter and Wavelab mastering software. Expensive and hard to learn, though.

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.