This is a really good question.
Here are the things that you need to study in order to become a successful System Administrator and end up with a high paying job
Everyone should have some basic programming knowledge. You can choose any programming language, it does not really matter. You just need to make sure that you are familiar with the basics. You can start with Python, Java, PHP or any other language.
Get some administration experience in Linux. Develop a good working knowledge of Linux using both the graphical interface and command line, covering the major Linux distribution families.
I recommend this free Introduction to Linux course from the The Linux foundation!
Learn the basics like the OSI model, clients and servers, protocols, IP addresses, network hubs, switches and cables, routers and firewalls.
As a good sysadmin you should know how to read and write BASH scripts in order to automate your daily tasks and speed up your deployment process.
Hope this helps,