Because of my bad Mp3 player (troubles with the hardware encoding with Lame Mp3 files), I'm looking for another very good codec in order to listen to my files without those bad clicks etc.
What's your advice?

Thanks a lot to everyone

try lame with CBR

http://www.hydrogenaudio.org/forums/index.php?showtopic=203&
see this thread for other switches

some players have problems with VBR and with high bitrate. this is most probably not an lame issue.