I have used 3 different Mini's over the years as iTunes servers. They all ran 24/7 with no sleep and the disks never spinning down. When I want to watch something, I don't want to wait for disks to spin up. 
On the Apple TV, go to the Computers icon, then select your server. From that point on, the only content that you will see will be local files on that machine (the AppleTV doesn't know anything about your NAS, it's functionally the same as a disk on the server).
You can easily try this out without buying anything. Just put some movies in iTunes on any Mac (you probably already have some) and turn on home sharing. You will then have an iTunes server, it's just that simple. You should be able to select it through the Computers icon on your AppleTV.
As far as using the AppleTV app (as opposed to "computers"), I am under the impression that it will stream your iTunes purchases from Apple's servers directly. I don't think it will access them on a local server, but I really don't know for sure. I just upgraded from an AppleTV 3, and there are a number of things that still confuse me about the new(er) models.
On the Apple TV, go to the Computers icon, then select your server. From that point on, the only content that you will see will be local files on that machine (the AppleTV doesn't know anything about your NAS, it's functionally the same as a disk on the server).
You can easily try this out without buying anything. Just put some movies in iTunes on any Mac (you probably already have some) and turn on home sharing. You will then have an iTunes server, it's just that simple. You should be able to select it through the Computers icon on your AppleTV.
As far as using the AppleTV app (as opposed to "computers"), I am under the impression that it will stream your iTunes purchases from Apple's servers directly. I don't think it will access them on a local server, but I really don't know for sure. I just upgraded from an AppleTV 3, and there are a number of things that still confuse me about the new(er) models.