Something like iTunes (free download from Apple --> http://www.apple.com/uk/itunes/
) Would be my personal preferred choice as you can simple insert your CD into your computer and then iTunes will rip all the tracks off it and will also try to find a matching list of track names (and cover artwork) from online sources. Then you not only have your music stored on your computer but also in a easy-to-use media player.
With regards to vinyl LP's then the process would be more involved with having to individually record each track off the LP and then import it into a media player. If we stick with the iTunes example, once you've recorded your LP tracks onto your computer you can then import them directly into iTunes and manually name the tracks and even add your own artwork (for the album cover) should you so wish. The difficult part in this is having a piece of software to enable you to easily record the music from your LP's. Unfortunately I cannot advise much on this area.