About two thirds as wide as it is deep, would be my preferred rough assessment.
That is, if it is 10 inches across, you want it to be 15 inches deep.
No difference indoors or outdoors, but if you live in an extremely hot place in summer, light coloured pots (white, light brown, light green) help to keep the roots cooler. Otherwise, a pot inside another pot will also keep the roots cooler, that is, the pot with plant and soil placed inside another empty pot of the same size so there is a double layer.
Most importantly, pots must be of sufficient thickness to ensure the roots are kept in the dark, clear plastic is a big no-no.
Pots that don't taper or have minimal taper are best. I can find no evidence that round or square pots make any difference.
No science involved, just close to 40 years of experimentation growing outdoors.