Again, Mac Mini and Apple TV are two COMPLETELY DIFFERENT THINGS.
Mac Mini - real computer, without monitor/keyboard/mouse. Runs OS X. Basically this is a good server to keep all your movies, music, videos, photos for your house on. This is not the ideal thing to hook up to your TV.
Apple TV - a streaming box. Should be one attached to every TV in your house. This allows you to stream content from your Mac Mini (or any other laptop/desktop/iPad/iPhone in the house). Also gives you Netflix.
Ideally, you'd have one Mac Mini like in your basement, and an Apple TV attached to each TV. Therefore, you add a movie to your Mac Mini, and all the Apple TVs in the house have it.
If you have only one TV, and your computer is in the same room as the TV, and never use your computer and TV at the same time get just a Mac Mini.
For any other reason, you need a server (could be Mac Mini or something else), and get an Apple TV for each TV.