If you convert mp3 files to some other format (say flac for example) you'll lose quality, so the only/best way to convert without losing quality is to convert to a lossless format (wav or something) which of course takes a lot of disk space and you won't get any better quality. When you rip a track from an audio cd, for example, it's got some quality. When you encode that file, usually a wav, into something lossy like mp3 or ogg, the file size is reduced but so is the quality: something is dropped off the file to get it smaller (and it's done in a way that you would hear as little loss as possible). But after that the lost information is lost, and converting to a format which is less lossy than mp3 won't bring that quality back because you simply can't get the information from nowhere
instead you need to get the original media (cds for example) and rip them again, but this time not encode to mp3 but to some other format like flac, preferably something that's more or less lossless, or at least less lossy than mp3.
If you burn audio
cds you only have one choice. If you burn data
cds, like mp3-cds, then you'll probably use the format where file size compared to quality is best for your needs.