If you're hosting from a computer inside your local network, you will need to forward the port that the particular service uses so that people connecting from outside your network can access the internal service. For example, you would need to forward TCP and UDP port 10333 to the IP address of the computer inside your network that was running the Team Talk server. This is not the best approach because from what I've heard, most Internet Service Providers significantly limit your upload bandwidth. This will be used to serve the content to people, and if it's too slow, your servers will be slow for folks who connect. You also may be introducing security risks by opening too many ports, although I'm not 100% sure about that. Question: When port forwarding, is it only a risk if you have an application currently listening on that port from the specific computer you designate? I.E. Is the port not open if you stop the service that listens for incoming data over it?

You can also put your computer into the DMZ or Demilitarized Zone. From what I can tell, this allows all traffic from the Internet to reach your computer. I wouldn't personally recommend this, since there's no telling what someone with malicious intent could do.

The problem with this first solution is that your home network and devices must be operating 24/7 or your servers will go down. This is why I recommend getting a VPS from a company like Linode. You pay a fee per month and get access to hardware that you can do anything you like with. The hardware is being maintained by someone somewhere else, so you don't need to worry about power or hardware maintenance. Most of these run Linux and that will be cheaper. I've heard of Windows Server VPS providers, but I've never used them as I have no need for Windows Server. Windows Server is more expensive because of Microsoft's licensing.

Anyway, once you choose a VPS, you can begin configuring the services you want. You will first want to install a Linux distribution and connect to it using SSH. This is 100% accessible because all output is conveyed using text and you type commands to control the server. You will probably want to do a few things to better secure your server such as creating a user account with limited permissions, disabling SSH log in using the root user, changing the SSH port, and configuring a firewall to block all incoming connections except the specific ones you need for your services, etc.

At this point, you could configure a web server using Apache, PHP and MySQL, run server programs for games, run a Team Talk server, etc. I'm not very proficient using Apache and PHP, but I may or may not get there one day. My website probably wouldn't be very visually attractive and I'm not paying someone to visually design it. For games, you will want to make sure that the game offers a standalone server application that's either command line based or has no GUI. You'll want to run Windows applications using Wine.