Inside each theme documentation section found at our support page you'll find information on the specific option as well as suggested resolution and file size for that image.

In general, keep in mind that Tumblr does NOT resize the custom images you upload via the appearance or theme options (with the exception of Avatar) and large files can slow down the load time of your blog and make mobile devises "freeze". It's recommended that you use JPG images with quality between 80 and 90 percent and/or you optimize your image before uploading with a tool such as (in other words keep the file size bellow 1 MBit).