Figure 1000 gallons for the first koi, plus 250 gallons for each additional koi. You could keep 5 koi in that pond with good filtration and aeration. They are very big fish, and three feet is a bit shallow for them, so I would be conservative.
For a mixed pond, you can substitute 4-5 fish-shaped goldfish for one koi. Mutant, egg-shaped goldfish are fatter and more delicate, so if you really want to keep them, they'll need more room. Also, they have so much trouble swimming that they don't do well with more agile fish. Orfe are a little smaller than koi, but are more active and need more oxygen, so count them as koi. They're also schooling fish, hence to be fair, you need at least three of them.
For a pond with only goldfish, figure 30-50 gallons per fish. 40 goldfish should be plenty, that will leave room for sunfish or other predators to help control the eggs and fry. Don't expect perfect control, though. I'd start well below the maximum with goldfish unless you've already arranged with a local pet store to take the extras. I'll guess sunfish should be counted as 1-2 goldfish, depending on their size. Keep in mind that if you have male and female sunfish, they'll breed too, even if they are different species.
As a general rule, the oxygen and filtration requirements of a fish go up with the square of length, assuming similar proportions. Hence, 1 24" koi would be equivalent to 4 12" goldfish or about 100 minnows.