Transferring cd tracks from an old device to a newly reformatted Mac on iTunes?

Merry Christmas, everybody! I switched from iPhone to Android earlier this year, at the cost of the music I had on my iPhone. Fair enough. Couldn't transfer the files from itunes to my external harddrive anyway because of Apple's formatting. Anyway, this christmas my mother gave me a new iPod Touch for me to have my playlist on (bless her heart), but there was an immideate problem: earlier this year, around August I believe, we had to reformat or reset our mac because it literally hadn't been updated in years, it was just so slow. The reason is my late father, he set up all the passwords and stuff, he really liked Apple and iTunes (literally 1st gen). And in true fatherly fashion, he forgot to write the passwords down for my mother. This has resulted in a fair bit of troubles for us, but that's beside the point.

So, now that I have logged on to the brand new iTunes 12, gotten a new password and everything, I noticed something was amiss. All of our old cd music was gone. EVERYTHING. The only stuff left was music I had downloaded on my old Touch and iPhone.

Thankfully, I found my dad's cd collection on his slim (or shuffle, I don't know, it's one of those slim ones with a selection wheel and a small screen, might be touch, no on-off-button, just a switch that activates/deactivates key lock). My question is this: how do I transfer/synchronize the music from my old devices to iTunes so that I can download it to my new Touch, without losing everything in the progress?

You could always try the 'backup' option? It backs up everything on the device onto iTunes? That's the only way I can think of.