Install on Mac Mini server?

Hi, I’m somewhat new to the WordPress(.org) installation process. I have my website Browser Beat up and running using the latest edition of WordPress on GoDaddy’s servers.

I intend on getting a Mac Mini server with Lion Server, and would like to run my website off of the Mac Mini. How would I do this, as well as make the server accessible outside of the network so that people can see it on the internet?

Please remember that I’m new, and I need you to be as descriptive as possible.

Thanks!