There is no accessible storage, only a small flash drive for buffering streamed content and a select amount of photos for the screensaver.
If you want to view your photo library or stream local iTunes content you need a computer on.
A movie streamed from your MB is over the local network. Renting on the Apple TV is streaming via the internet. For instant playback you need 6mbps (for 720p) and 8mbps (for 1080p). Check speedtest.net
As there is no accessible drive, if you access other content while your film is loading it will be flushed and require a reload.
Check istumbler or net stumbler for interference