OK, lots of software available, but not all of it is "good".
MP3 Compression -
Many MP3 Compression techniques available, but only one stands out as giving you copies that are completely indistinguishable from the CD itself. And that is the LAME MP3 codec. Do a google search for LAME MP3 and you will find a free download for the codec, as well as a plethora of info as to why it works so well. No one who has used LAME bothers with anything else.
If you compress with lame, you will not be able to tell the master from the copy, no matter how much of an audio nut you are. No other MP3 codec can claim this.
CD Ripping -
Any ripper should be OK, just make sure you are porting the compression out to the latest LAME release.
I personally use EAC (Exact Audio Copy). It is the only program I am aware of that rips a true copy of a CD, giving many retries for missing data, instead of just copying skips and pops into the MP3 file. If your CD ROM drive supports C2 level error correction, EAC does to. This can actually fix some o the data coming off of the disc if it is damaged. If your drive does not support C2 Error correction, EAC will just do the best it can.
I had several CDs that were rather old, and hammered. Some looked like they had been treated with sand paper. I ripped them with EAC, and they are perfect. One of them took almost 4 hours to rip, but I did get a perfect copy. My drive does support C2 error correction.
EAC is slow, the average disc take a few minutes, but it does a great job.
Both EAC and the LAME mp3 codec are free downloads. EAC can be tricky to setup and isn't the easiest thing to run, but to me the results are worth it. It does, like many other rippers out there, connect to freeDb and download track info so you don't have to type it all in.
Cheers,