Your cooking pot needs are determined by what, how, and for how many you cook. When I travel alone or are at least cooking for only myself, I can get by with a recycled 12 oz Vienna sausage can for a pot and plan some of my meals as the "boil water and dump" variety and eat the rest cold.
If I'm cooking for more people or anticipate melting snow/ice, I look for a larger pot. I imagine if I were to do a long-distance hike and intended to resupply by purchasing food in towns, I would want a larger pot, as well. You CAN get by using a 25 oz beer can (Fosters, LaBatts, and others) to cook a package of Lipton Noodles with some tuna and green beans. It is a close fit, though, and the shape makes for an inefficient ratio of pot bottom to stove/flame. Many hikers got to like the "X-Mart Grease Pots." I haven't seen one in a WalMart or KMart for a couple of years or more. The K-Mart pot had an outward-rolled lip, which made it more desirable. These were little more than thin seamless cans with a strainer and lid. If you can find one, it will be wonderfully light but thin enough to also be easily crushed. I loaned my WalMart GP to a co-worker's son. Gone! If you don't mind replacing your pot occasionally and don't do a lot more than boil water, you can get by with a recycled can. I've used them when I've camped/backpacked and tossed or given away before flying home.
Cheap sources of a more permanent pot: yard/garage sales, thrift shops, "dollar stores," and used gear lists. Some people buy a cheap, light pot intended for home use and cut off/unscrew the handle.