Two numbers do most of the work: volume in gallons and depth in inches. Volume decides how long the pot holds water and how much root the plant can build; depth decides which crops are possible at all — carrots and garlic want twelve inches whatever the width, lettuce is happy in six.
Material matters less than people think, with two exceptions. Terracotta wicks water out through its walls and will halve the time between waterings on a hot balcony, and undrilled plastic — buckets, decorative pots with no hole — kills roots faster than drought does. Everything else is preference, weight and price.