Sysadmin here as well. This is solid advice. You specified telecom in an earlier post - do you have a telecom product in mind?
Asterisk is an open source VoIP telecom system that you can get going to play around with. If you're looking at enterprise class stuff you are pretty much stuck until you get on the job - that stuff is expensive and usually requires proprietary equipment.
Do you have an OS in mind? The advice specified a domain controller which usually implies Windows, which isn't bad in the business world
but might not be in line with your goals.
Learn to script things. If you choose Linux, bash, if you choose Windows, PowerShell. If you want something that does both, look at Python.
If you want hardware recommendations you can get some cheap stuff on ebay. Decent Dell R710s are about $400 and will allow you to run Nutanix Community Edition which is a virtualization product that will give you some enterprise level virtualization tech. VMware used to have a free edition as well, I don't know if they do anymore. You can of course do it on your local machine with VirtualBox or similar as well.
The book that lain recommends has a third edition now, which is more in line with the cloud-based world we now have to live in. Matter of fact, get yourself a Safari Books subscription; it's expensive but will get you a whole load of books that will be useful to you. It will also help you with coding.
Coding - what language are you looking at? What do you want to accomplish?
Packet Tracer and other programs might be a bit overkill unless you see yourself going in to the networking field. If you don't see yourself handling the network equipment I wouldn't worry about it. If you do, Packet Tracer is a solid choice.
Sysadmin is a feast or famine career, either there's nothing happening or your hair is on fire. But, it's OK overall.