Almost anything that applies to Ubuntu will apply to Linux Mint as well since it uses the same base and repositories as Ubuntu.
If you're completely new to working with audio on Linux drop by the
Libre Music Production website and start your journey there. And while there, take a look (via their links) at
KXStudio distro. That's a very good starting point, and has everything you need "under one roof" to get you started.
If you plan on doing a lot of audio work, it's generally a good idea to have a dedicated machine to do it on. You'll basically want a machine whose OS is stripped down and optimized for audio software. And in the case of Linux, probably also running a 'real time' kernal to minimize the potential for latencies when recording or producing music.
That's not as scary or expensive as it sounds. Because there are music distros that already have that all done for you - and many of them can be run as a "live" environment (i.e. booted and run of a disk or USB key) so they won't need to be installed onto a harddrive before you can get familiar and do some work with them.
But before you go that far, best follow the learning steps Libre Music Production suggests on their website. There's a lot to learn. And it's important to have some of the basics (like JACK, doing proper backups and maintenance, etc.) under your belt before you get too ambitious. Slow and steady wins the race with this stuff. No matter how much you already know about computers or your operating system.
As far as Linux hosted DAWs go, there are several that are native, and the inexpensive and popular Reaper for Windows which runs well under WINE on a properly configured Linux box. I personally like the
Invalid Link Removed software. But it's
not free ($80) - and it can start to get expensive once you start adding additional optional modules to it. Fortunately, they regularly put the add-on modules on sale for half price so it's not necessarily as expensive as it looks at first. And there are other less elaborate (i.e. traditional studio looking) DAW choices to look at as well.
And...that should be enough to get you rolling.
Luck!
