Animation is no doubt your best (quality) compression so far as factory installed codecs, although your file size won’t drop that much. H.264 will drop your file size drastically but your footage will lose a lot of its quality. Simply put, all of your shadows will disappear and your image will look muddy.
When you export from PP, try changing your pixel aspect to square and use one of the following dimensions; 1920×1080 or 1280×720, depending on whether you shot 1080 or 720.
Let me know how it goes.
William