how will the dimensions of my tank affect what fish I should have?

longer, shallower tanks are better for active, fast swimming schooling fish like danios, barbs, and rainbowfish. deeper tanks are better for taller fish like angels and discus.

I think the point is, as said by rbishop, that the most important parameter effecting how many fish you can stock is the surface area of the tank, which dictates how much gaseous exchange can occur (oxygen levels).

Probably therefore the least important dimensions for most fish is the height of the tank, as this doesn't add to the surface area. So the mistake would be to think that a tank which is 36 inches long and 36 inches high can take as much stock as one which is 72 inches long and only 18 inches high, if both tanks have the same width, just because they are of equal volume.

Then, if you want active fish, they will need room to swim, so long tanks. if you want territorial fish, they will need room to form territories, so long tanks too. So its not perhaps so much that shallow tanks are 'better' its just that in most cases the dimension to compromise on is height as opposed to length (allowing also that some fish prefer shallower tanks anyway e.g. labyrinthine fish like gourami, bettas).

Surface aggitation is not the only way to have gas exchange- live plants also consume co2 and produce oxygen. What fish can work in any given size tank is primarily a function of 3 factors:

1. Max length of the fish. A two foot long fish needs space in which to swim plus a wide enough tank to be able to turn around in. A further consideration is how fast they swim and how active they tend to be. A two inch oto needs a lot less space than a 2 inch danio for example.

2. Territoriality- more space provides more places to hide or to stake out a territory. Schooling fish need less space than ones that stake out their own territory.

3. Temprament- fish that dont get along need a lot more space than those that do. Also eating habits are a sub-factor here. Carnivores vs vegetarians as well as how agressively they go after food. Spawning behaviour may also be a factor.