What software did you use to burn the MP3 tracks back to CD audio? Most likely, its (embedded) MP3 decoder wasn't any good. For example, if Winamp can play the VBR MP3 stream fine, then it can write it out to a .WAV file just fine. Just about any CD burning utility on the planet can adequately burn .WAV files to CD audio (in other words, as long as its decoded properly, there shouldn't be any problems). I never go from MP3 to CD audio, but I imagine this manual (file by file) method is no longer practiced.
As far as CDRs go, I can't speak for which brands are best for picky stereo CD players. But Taiyo Yuden CDRs are widely considered the best CDRs readily available. These are commonly rebranded for sale in retail channels; just about every other weekend you'll see a good deal on FujiFilm TY CDRs. Most of us regulars in the Hot Deals forum will gladly pay the nominal price for FujiFilm CDR media after rebate, rather than pick up spindles of cheap brand X. Personally, I'll selectively buy spindles of the free after rebate CDRs from time to time because I don't always need high-quality media.
Using high quality media is definitely recommended for archival purposes (i.e. anything you want to reliably last for years). Final comment: note that in almost all cases, any media will burn without errors on contemporary CD-RW drives. However, there is test equipment that can assess the actual quality of the media itself; Taiyo Yuden blanks are amongst the best when it comes to the underlying error rate of the media. Since there's error correction built-in, cheap media still works for most uses, but it may not stand the test of time and wear.
As for the original question, CBR 320 is probably a waste of bits. LAME's highest quality VBR should give very good quality for the bits. Otherwise, if you were insanely quality-sensitive, then you wouldn't be choosing a lossy encoding format.