(I think now it can only do music), but it will show up under computers on ATV's without a Mac switched on. The other way is the traditional way which means having iTunes open on a computer. In order for iPhones and iPads to access iTunes you can install DS Audio app (from Synology) onto the iOS device or use the traditional method which is iTunes sharing (and I think really the best solution).
As you stated, sharing from the NAS directly will only support Music. If you want to use the Apple TV in the way it is intended, you must be running iTunes on a computer (Mac or PC). There are some work arounds, one of which involves running an app on an iOS device. I did not want to do this. With the Mini running iTunes all the time, the Apple TV can always access my library by going to the "computers" icon on the home screen. You can do the same thing by just letting iTunes run on your PC.
Where you actually store the media (direct attached or network) is sort of a secondary issue.
When I was talking about connecting a disk to the airport extreme, I was referring to directly connecting a disk to the USB 2.0 port on the airport. Of course you can connect a NAS to the airport as well over ethernet. That should give much better performance than connecting a disk to the airport on USB.
Hopefully you'll find a solution that suits your need at a reasonable price. But if you want the full function of the Apple TV the way it was intended to be used, you need to be running iTunes on a computer and have home sharing enabled. I think you'll find that the least expensive way to set this up is just connecting an external USB disk to your PC. There are other advantages to having a NAS of course.
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If I did not want to keep my PC on all the time with iTunes open, then I am wondering what I can do instead.
That's the problem, you will have to use one of the work arounds, like an iOS app that accesses the NAS, then uses Airplay to send the movies to the Apple TV. I gather there is an iOS app from one of the NAS vendors that you only need to run once to connect initially to the Apple TV, then it will continue working without the app.
This all seemed kind of kludgy to me, but maybe it would be a good solution for you. As I mentioned above, you could use an old, cheap computer and just let it run iTunes all the time if you don't want to do this on your main PC.