You have some flexibility when designing your layout for mugs. Although the default crop box in the cart is fairly square, if you select "cropping: None", we'll do our best to fit the image around the mug if it's a landscape-oriented image.
Minimum photo resolution for mugs:
11 oz mugs - 600 x 450px
15 oz mugs - 640 x 475px
Using a panoramic image:
Currently the lab cannot wrap handle-to-handle, but they are pretty close on the 15oz white mug if you use an image with a 3.5x8.5 aspect ratio. For an 11oz white mug, one side of the image will still be a few inches away from the handle, but your best bet is a 3x7 aspect ratio. Ditto with the 11oz black mug, though this same aspect ratio ends up wrapping somewhat further around the mug than in the 11 oz white mug.
An example of a 3x7 aspect ratio image: 1500px tall by 3500 px wide.
Here is the size of the cropping area in the shopping cart:
I just took a crop from an image, and put it on a canvas that was the proper size, then added the text in photoshop.