You can't beat the knowledge you get from setting up your own server. Most of my skills have come from repeated ( and I mean many many times) installs of Lamp stacks and Moodle. My preference is Digitalocean for both low price and ease of wiping and starting all over. There are some excellent tutorials which will take you step by step through the install. At first the instructions are a mystery but soon you can understand why you are doing that step
I started with Debian and switched to Ubuntu. I didn't notice any difference as Ubuntu is Debian based. I have never tried Centos as there doesn't seem to be any Moodle documentation as good as the Ubuntu Step by Step guide. Strength of support from tutorials and forums are I think the main reason for choosing an OS.
I run my production instance on a Digitalocean droplet. Something to be said for tinkering in the same environment before deciding everything is robust and ready to face students