AAC should be able to be played on Linux ‘as is’. I tested a .M4A file (AAC audio data in MPEG-4 container) and Rhythmbox was happy to play it.
If you are going to convert, converting to FLAC may be preferable to MP3. Rhythmbox is happy to play a FLAC file. (Both AAC and MP3 are encumbered.)
If you are doing a bulk conversion then soundconverter is good e.g. happy to convert .M4A to .FLAC.
That’s not small. How many files is this? Expect it to take a fair amount of time just to copy the data, never mind about converting formats if you decide to convert.
You aren’t realistically going to do that via CD. That would be hundreds of CDs! (if done as standard audio CDs, and still a total pain if done as data CDs)
Unfortunately I won’t be able to provide any step-by-step instructions for a Mac.