Intrigued by all this yesterday I found my 2metre 3.5mm -> 2 RCA phono lead from my laptop bag and plugged it into 'line in' on the laptop and 'tape out' on the back of the amp.
I tried Audacity (free download) and did not like it. Way too much faffing around and aimed at the home musician/mixing & editing guys more than someone just wanting to digitise analogue media in good quality.
This morning I downloaded the trial (5 albums trial) version of
VinylStudio by AlpineSoft (£18 for paid up version) and it is superb.
Very easy to use and geared up for excatly what the OP and I want to do (digitise LPs or cassettes).
Once I had decided upon a few things like MP3/WAV quality and sampling the rest was just logical step by step stuff, guided all the way with simple explanatory windows and 'bubbles'.
I have just finished 'recording' my first test track from LP and imported it as a file to iTunes and played it back.
Superb!
I am going to pay for the software and have fun cherry picking fave tracks from various albums to put in iTunes.
This for me is not to play whole albums (I have the turntable for that) but to add tracks to various playlists (Jukeboxes as I have them named) for casual/background listening.
[Edit.. Ok I now know why the quality was a bit good. Track info on iTunes tells me the track is 1411kbps (16bit/44.1khz) WAV and the track size is 44.6 MB for a 4 minute track!) Think I need to tweak that down a bit. 320kbps should do.]