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Apple TV (2nd and 3rd generation) are set by default to provide the highest resolutions available from iTunes Store.
If your Internet connection is too slow to quickly start playing High Definition movies or TV shows, consider changing your iTunes Store Video Resolution preference to Standard Definition.
To do so, from the main iTunes menu, choose Settings > iTunes Store, and toggle the "1080p HD" or "720p HD" option to "Standard Definition".
For troubleshooting on this, take a look at this article:
Apple TV (2nd and 3rd generation): Troubleshooting playback performance
Hope this helps,