On tests I conducted a while back, the LAME encoder is in fact better than the built-in Frauhofer encoder used in iTunes, so something like MaX might be an option for you if you're determined to encode to MP3 at all.
Personally, I left MP3 years ago in favor of what to me is the superior sound of AAC. You can hear the difference most obviously on high-hat drums and a few other types of sounds. Since most of the music I have in iTunes is ripped from CD, I have an "ultimate lossless backup" if you will and am quite satisfied with 256kbit AAC, though of course I don't have a $10,000 audio setup or anything like that.
When I switched to AAC I was worried that nothing else would ever support it, but those fears appear to have been misguided. MP3 is still more widely accepted than AAC, so if you want near-universal device compatibility then MP3 is still the way to go, but I wouldn't play music on something that I can't hook a compatible AAC-playing device to, so it's a non-issue to me.