I want to burn some music onto disc for posterity though I would also like to listen to the music whenever I choose. It seems that if I want the best and unchanged quality I must create a data cd and if I want to listen to the music through a stereo then burn a second disc as an audio cd. correct?
No. Your music (I have no idea what format it's in) in iTunes will be converted to a LOSSLESS codec during the Audio CD process so there is NO loss or compromise of quality whatsoever.
I would like to know the best settings to burn an audio cd.
There no "settings" for an Audio CD. It's a standard format, no customization. Google it if you want the full technical specs.
Will an mp3 cd have better quality?
No. If the music is not already in MP3 file format (ie heavily compressed), then it will get substantially WORSE being converted to MP3. If it is in MP3 format, then nothing will change.
In the application Burn I can change the bitrate if burning an mp3 disc. Should I adjust this? I understand a higher bitrate will use more memory on the disc?
"Memory" refers to RAM. Discs don't have RAM. You mean space. Yes, a higher bitrate will take up more space. But again, if your music is already in a compressed format, changing the bitrate on an MP3 disc will do *nothing.* It does not magically re-imbue your compressed files with more quality.
If the files are presently in an UNCOMPRESSED format, then changing the bitrate on an MP3 disc will help (higher bitrates obviously sounding better), but you are still taking an uncompressed file and turning it into a HEAVILY compressed file so you will still lose sound quality by making an MP3 disc.
I read burning at 4x speed may be best or is this just dvd? why is this?
First, don't believe everything you read on the internet.
Second, older burners are less prone to errors if they burn at the slower speeds. This is also true for video burning. Modern burners this is not really an issue.
simply, how can I ensure the best quality/least quality loss on an audio cd?
Burn an Audio CD. There is no higher standard unless you count DVD-Audio which is an entirely different, incompatible and unrelated format generally intended for 5.1 and higher multi-channel sound.