[hat and beard]

I'm moving next month and I've decided to leave the vast majority of my records behind, but I'd at least like to have them digitized and living on in my computer. I'd also like to upload some things to the internet. SO...
Anybody have advice on how best to go about recording vinyl records on to my computer box? I know I can just plug the headphone jack in my stereo directly to the microphone jack in my computer, but is there a better way to go about this? Is there free software I can use to record? Is there any hardware I can buy (soundcard?) to improve sound quality. I'm quite useless with all this technology stuff, so any help would be appreciated.