First remix!

I was wondering what kind of software to download to start remixing songs. This is my first project and I'm starting with a mac and some ideas.

Full context of my project is to make a club style mash-up of songs from the musical Titanic with songs that I think would be fun to drop into. Such as, at the end of The Blame when they are all singing "My ship, no one elses..." cutting to Gwen Stefani's B.A.N.A.N.A.S. This is to play for the cast and crew at the closing night party, just for fun, not any streaming or resale.

I do not know how to convert audio from Apple music or any other streaming service, or even youtube? to make this work. Or what kind of software to mix this on, like garageband or something similar? So any guidance would be great!