I started off in the tech field about 13 years ago having computers as a hobby much like you describe. Starting off, I would look at A+ and making sure you understand the basics. Setting up a small network in your home, setup an AD domain and learn from there. Learning basics on lan/wan technologies is also very important.
Microsoft offers some free courses from the desktop type support to server technologies. These won't cost you any money and offer a lot of good information.
Virtualization technologies are becoming more important for all types of businesses, and most hypervisors can be downloaded for free and the management tools can usually be downloaded for free on a trial basis. It's a good way to get your home lab going.
As others have mentioned, I can't imagine doing helpdesk work for a long period of time. I did it for a couple of years and found it too repetitive but I find it an important first step for any seasoned support person.