If a "new Earth" was found, I'm assuming this would be a planet that existing or future observing instruments had found to be about the right size, right temperature, and having the presence of liquid water.

Such a planet might be ripe for colonization, but I would hope the human race spends some time observing it with probes or even local manned space facilities (assuming some breakthrough in transportation).

If such a planet had life and an ecosystem on it, it would be literally priceless as a scientific find in its untouched condition. At some point, it may be feasible to colonize it, but not for quite some time. If ever.

For what it's worth, if it were up to me, I'd watch Mars for some time before I opened it to major colonization, too.

Personally, I think colonies on terraformed Solar System worlds and deep space asteroid and O'Neill colonies have a lot more potential compared to interstellar colonization.

At any rate, while colonies in space and in other solar systems are a vital long-term requirement for species survival, it's not a solution to any of our near-term problems on Earth.

Your point about the psychological impact is a very good one, though, and only the discovery of extraterrestrial life would have more impact.