I've experimented around with this for the last year.
My original goal was to simply burn the LP's to CD for listening to in the car. I started out by hooking a Dell laptop up via the tape out on my amp by way of an RCA to mini-plug adapter and recording using CoolEdit software. I wasn't real happy with the sound quality though - most probably due to the soundcard built into the laptop.
I then purchased a Pioneer CDR burner which worked out well - but I did end up making quite a few cdr-coasters by not setting levels correctly or pressing the start / stop button a bit too late, and so on.
The best way I've found so far is I purchased a Yamaha CDR-HD1000 CD/HD recorder for $300 shipped from vanns.com http://www.vanns.com/shop/servlet/item/features/534499582
What this device allows you to do is record straight onto a 20Gb hard drive within the unit - so if you mess up you just simply erase it and start again. You've got all sorts of editing ability once it's on the drive too. You can do fades, erase portions of the track, and a lot more.
Once it's on the hard drive as you like it you do a high speed direct digital rip of it to an CDR-Audio and you're done! If you want it in MP3 you can rip it to your hard drive from teh CDR and convert it with MusicMatch, etc. and dump it to your i-pod.
The Yamaha unit does a great job and the sound quality is fantastic. I've ripped hundreds of LP's and have been very happy with the results. At $300 shipped it's a steal considering its original MSRP of $1000.