"Linux System Administration" is quite a large subject.
Administering a Red Hat based distribution (like Fedora, CentOS, Red Hat Enterprise Linux) is similar, but a little different to a Debian based system (like Debian, Ubuntu, Raspbian) and also different from other bases, like Arch, Alpine, Android or distributions of Linux packages installed on routers, NAS and other embedded devices. There are also similarities to other Unix based systems, like FreeBSD, NetBSD and Solaris.
While differences may be just in how the packages are created and installed, you may also see a difference in how systems are installed, where configuration files are stored or how services are started and stopped.
If I was starting this fresh, I'd start with something where there's lots of available documentation for you (which Ubuntu and Arch both excel at) and which system you are most likely to find support in your communities (so if you have a friend, neighbour or relation who uses Fedora or CentOS, it's probably best to start there)... but, remember that there are LOTS of similarities, and many distributions use the same underlying packages, so while it's important to start with something it's more important to keep learning!
I personally use Ubuntu for my servers and services, and I use Ansible to administrate my servers, but I've worked on Debian, RHEL and NAS appliances, and the basics translate across all of them!
Good luck to you!