A question before doing anything
 

I want to set up my own private server to play with my friend. I'll connect to my server on a computer on the same home network. Here's my question : will my friend be able to connect on my server from his computer at his home?

You'll need advanced networking skills to get it to work. If your server won't have an external IP, you'll have to set up a virtual network with your friend's computer, either with a dial-up modem connection (Don't laugh, I got it to work), or tunneling through the Internet. It won't be easy, but it can be done if you know what you are doing.

Well, my server IP will be something like 192.168.0.104, but what if I setup a virtual server on my rooter to foward all packets coming from a giving port to that internal IP? Would it be sufficient?

I don't know anything about routers. Someone else may be able to help, though.