The best codec IMHO still remains the original Fraunhoffer (sp?) codec. Unfortunately, that still remains the the one which carries a licensing fee with it, so it's not easy to find on freeware. I *think* this is what iTunes uses, however, so there is a free source for it right there.
My favorite free one used to be the Blade engine, using a version of the old ISO codec. Not as sharp sounding as Fraunhoffer, but it's coloration seemed to almost add an analog-ish sheen to the recording. I don't think that's available any longer, though; I'm not sure, but I think there were legal issues involved somehow that took that off the market. Maybe someone else knows better than I about that.
But I also have to say that in my limited world of experience with MP3 encoding, that the only times I have experienced any really audible - meaning to the casual listener on the average playback system - problems with MP3 encoding in any codec has been with mixes that had some real problems of their own to begin with.
G.