You have some flexibility when designing your layout for mugs. Although the default crop box in the cart is fairly square, if you select "None" for your cropping option, 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 can't wrap an image handle-to-handle, but they come pretty close on a 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. An example of a 3x7 aspect ratio image would be 1500px tall x 3500 px wide.
We took a crop from an image and put it on a canvas that was the proper size, then added text in Photoshop.