Depends on what you're hosting...but 16 is a good start.
What games you planning on hosting and playing?
What OS are you planning to use? You might consider virtualizing a server that runs inside your OS that is dedicated to host games (a la MineOS on Turnkey Linux is one I use to host 5 MC servers with ease in VM form...).
If you are going to be hosting game servers, get familiar with commands and command line interface regardless of OS, understand network terminology and functions and set a static IP address for your PC/server. Know how to port forward from your routers firewall.
Also consider a dynamic DNS service if you don't have a static internet IP address. I use Afraid.org's free dynamic DNS service and have my router check in anytime my ISP renews my public IP address.
Understand that there's a lot involved for hosting a server at home. Most have a dedicated device...which is why for you I mention virtualization. It'll act as a physical system and you run it in your OS, assign it virtual CPU cores and dedicate some RAM and HDD space to it and go. Could be nice to not clog your main OS with extra server shit...
Windows 8 and newer can take advantage of installing Hyper-V as a feature...and its the same virtualizer that Windows Server uses. Would be a great place to start...fire up a VM, install an OS and game server services, link it to a virtual switch that binds to your current NIC or one you add dedicated to it. Heck you could play while hosting and it'd be workable. Though I'd run a dedicated storage device or array for the hosted services...keep your gaming stuff separated from the server stuff. Then if you're ever done with it or move to a better dedicated solution...migrate the VM and free up resources on your PC. Even shutting down a VM will free up CPU cycles and RAM...that dedicated hosting will not. Plus hosting various games on one system gets messy...do that shit virtually and keep your gaming rig clean.
There's of ways to go about this and I hope we can all give you some direction to decide if this is right for you.