If you are keen to copy music/convert music to MP3 from your own collection of CD's to be used on your own computer than you can take the following two routes:
dBPowerAMP: As Floppybootstomp has suggeted, it is a very user friendly program and not much input is required from the user. It does most of the things automatically for you and does it very well. This also is the quickest way of converting your music to MP3. I always recommend this software to those who want things done quickly and without going into too much detail.
Exact Audio Copy (EAC): This is my preferred choice always for converting my collection to MP3 for my own listening pleasure on my PC when I am working. However, you will need the latest Lame encoder plugin and you need to configure the program to do the conversion to MP3 for you. Some time back I created a thread giving full information on how to go about using EAC+Lame encoder and enjoying the best quality MP3's. This combination produces very accurate conversions and I have personally tested it extensively and so did many audiophiles who use nothing but the combination for creating MP3's when required.
Here is the link to the thread I created which you can use and see for yourself how good they sound on your system.
Highest Quality MP3's
Enjoy!