Hero banner: 1920 x 700px (1920 is really a minimum width for full screen images, anything less will scale up on the majority of monitor sizes and look poor)

Hero banner (thin): 1920 x 600px (or same as above for nodes hero banner field.)

Card overlay: 640 x 480px

Card: 480 x 480px

Node teaser images: 

Minimum: 480 x 480px displays nicely  inreferenced in Cards.

Recommended: 640 x 640px so a better crop can be made by image styles.