Look at it differently. What size will your animation be rendered at. Let us say you are going for a high quality render, using 1024x768 pixels, or something equally large.

If you are making a box, what percentage will this box take up on the final image. If it will fill the entire screen, then you will need a texture map that is at least 1024x1024 (1048576 pixels). But if this box will only take up a quarter of the screen, then you can get away with a texture map one quarter the size, so 512x512 (262144 pixels, which is one quarter of the large map).

Pixar, masters of animation, never use a texture map bigger than 512x512, and mostly use shaders. 

Always keep your texture maps in the sizes 256x256, 512x512, 1024x1024 or 2048x2048. Larger than this they take up too many resources, and these sizes, by the way a computer calculates, render and place less of a strain on resources than odd sizes like 2000x2000 or sizes that are not square like 2000x1000. 

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