Native?

Lately I've been wondering about the point at which a species becomes native. House finches, for instance. They were indigenous to western North America before European settlement but were brought east by humans. They are neither Asian nor European, so can they be considered native in West Virginia? Mockingbirds and cardinals have expanded their ranges on their own, perhaps as a result of climate change, so are they native to the North? How does a wildlife gardener decide which species to encourage?

And given how many native songbirds eat dandelion seeds, and given that dandelions are perhaps our most common wildflower, do we still have to consider them an invasive species?