The only thing missing from that equation, and possibly the reason your recordings sounded bad, is a phono pre-amp. Without going too into the specifics, vinyl is pressed at a different level, volume and eq-wise, and you need something to bring the sound back up to 'line' level. You should be able to get a cheap one for around $20-40US.
If you have a dj mixer, running the signal through that first will also fix the problem, as would a home stereo unit with a 'phono' input.
The other alternative is a USB turntable, but the reviews Ive read on those havent been stellar just yet.
Hope this helps.
Oh, and there is a free program online called Audacity thats good for recording simple stereo audio like that.