How much broadband data does Apple TV use in the menu screen?
If you consider a movie to be changing data 24 frames per second and compare the size of the menu art compared to the size of a movie screen you will quickly realize the menu items are negligible.

You will blow through a months worth of menu data in less than 4 minutes of a TV show through netflix or one short youtube video.

Do watch your data consumption - streaming music is moderate use - streaming video is heavy use.