if you want the best quality, it's best to get a preamp for it...
OLD record players will need a phono preamp for it (aka, a phono input in a reciever, which boosts the levels a lot louder). newer record players (some of them) already have that, so you can plug it into any aux input in your reciever, or say - your computer's line in? ha.
i know this, because i had the same probablems you had.
however - if you wanted - i dont see why you can't just buy a cheap preamp (like an audiobuddy or even cheaper! ha), and plug the record player into that (you will need 2 inputs, left and right!), and then go to your comp's soundcard.
just remember, your soundquality will be as good as the cheapest thing in your chain. so it just depends how intense and anal you want to get about this!
i mean, you COULD just plug the record player into your comp and be fine...right?