Your understanding of the designations (F0, F1, F2, etc.) is right on the money. F0 fish, at least in aquarium-speak, are wild-caught fish. F1 fish are the captive-born offspring of an F0 pair. F2 are the offspring of an F1 pair.....and so on....and so on.
One school of thought is that as you continue to captively-breed fish generation after generation, the resulting generations begin to lose some of the color intensity and other characteristics of the wild-caught types. On the other hand, captively-bred fish do tend to be (in general) a bit hardier and more adaptable to a wider range of aquarium conditions than their wild-caught ancestors. You have to strike a balance somewhere, I suppose, between the appearance of wild-caught fish and the hardiness of captive-born fish and I guess an F1 or F2 generation fish would come closest to that balance.
-Joe