I want the best quality mp3's possible and I don't care for file size. Will using CBR sound better than VBR ?

If you truly don't care about file size then you can use 320 kbit/s CBR (the maximum). Whether that will produce the best possible audio quality is not very clear - there've been some tests (click the "analysis" button) showing that lame produces better output at 256 kbit/s than at 320 kbit/s.

If you don't go to the extremely high bitrates, it's generally agreed that VBR produces better quality than CBR at the same bitrate. The idea is that you put your bits where they matter. On the other hand, VBR uses psycho-acoustic models that decide which bits of the music you can hear and which you can't (to decide what to throw away). If these models are wrong, then VBR may be reducing quality.

Recommendation: Exact Audio Copy for ripping, LAME for encoding. Use 320 or 256 kbit/s, or the highest VBR rate.

Borislav