I can tell you right now that capturing and training animals will, after a looooot of animals, get your civ very close to domestication but will never get you there. Toady's stated that until he programs in being able to alter what a civ has on the embark screen, there is no way to fully domesticate a species, because doing so would add them to the embark screen for future fortresses in that world.
It doesn't actually need to be all that many distinct animals - when I start setting out trap lines in the caverns, I usually pick up one or two weird beasts. At no risk (beyond autopauses) you can just tell your dwarves to train them right in their cages. They never end up very well trained, since only completely wild animals can be trained in a cage, but it happens automatically, so after a few years of keeping these caged animals around your civilization eventually gains familiarity with the animals. If you do start getting lots of animals (crundles) you can tame and then butcher them, rather rapidly becoming familiar with their training. Ironically, the animals I actually domesticate are the ones my civ doesn't necessarily get familiar with: I repeatedly train the wild breeding stock until young are born, but the young only need to be trained once to become completely tame, and *their* young don't need to be trained at all. So unless I keep the wild-born original animals around, I don't actually need to do that much training.
If ever civilization-level domestication becomes possible, the criteria need to be carefully thought out. Simply having lots of experience training animals does not get your fortress any tame animals, and you don't need to be any good at training a kind of animal to get a tame one - even aside from buying animals from traders, all you need to do is get the mother trained at birth, and train the young, and you have a tame animal. I'd like to see the criterion be "your fortress has at least n tame male animals and m tame female animals", and then later forts could start buying them from caravans.
Of course, caravan animals are going to be generated afresh, so giving them plausible ages (matters for cave dragons) may be tricky. Plus if your fortress starts selling tame giant war tigers soon every civilization will buy them and they'll start appearing as invaders/caravan guards/pulling wagons/pets of visitors. (Or rather, if they don't, it will seem like a weird lack in game mechanics.)