Well, for one thing, Android IS Linux. If you unlock/root your phone, you can do many things... or you may make it more exploitable to bad guys. I used to install custom ROM's on a Google Nexus 4 a long time ago, and it was fun for me, but it took some learning to get started. I now have a Google Nexus 6P and I've left it as stock Marshmallow. The Nexus devices are usually some of the easiest to unlock and root.
I'm rusty on what's current in that area though. There was a lot of talk about Ubuntu Touch on phones and tablets, but I never installed it and don't know anyone who has. I don't really classify ChromeOS or FirefoxOS as a full Linux distro any more than Android (and maybe less so). Many phones cannot be unlocked/rooted... so whatever you have, you need to check out what can be done, unless you will be shopping for a new phone to pursue this goal.
Cheers!