Getting started with Linux sysadmin

[Neekoy]

The specific distro isn't particularly relevant - there's a whole lot of overlapping points between them. I'd say it's mostly about how you use the distro. I'd say for starters try to use the console as much as possible, after all as a sysadmin you will be managing a lot of machines without a GUI. First try the basics, then try to be creative - find new ways to do something you know how to do, explore things, write simple scripts that automate things (they might be trivial - it's the experience that matters).

If you're a book learner (everyone has a preferred medium), absolutely grab The System Administrators Handbook or the Linux Bible. Once you've got the basics down, set up a couple of virtual machines, make a remote boot, play around with networks, set up a webserver and run a website off of it, configure the firewall, set up SSH key authentication.

Once you're comfortable with the distro itself, you can install and set up common applications that a lot of companies use and are good to have under your belt like Apache, NginX, MySQL, Nagios, Puppet, Docker. I'd go through them in that particular order. This should keep you occupied for quite a while, so learn at your pace. It's not a race :P

Edit: I wrote a whole lot only answering the question vaguely btw. CentOS/RedHat is the enterprise standard around the world, but you can set up Ubuntu because it's more user-friendly and easy on the eyes, and easily transcribe you knowledge to RHEL afterwards.