And no, it's not a simple matter after budget priorities either. Physics, bitch.
http://www.antipope.org/charlie/blog-static/2007/06/the_high...
And thus a long slow boat to the stars starts off as simple resource extraction. Sure, long term we might only be looking for gas giants as a ready supply of fuel vs planets to live on but there are other paths to the stars than a one shot moon landing style.
While that is clearly possible, it remains an endeavor for which all but the very closest targets (Moon, Mars, Venus) remain years away. I don't know that anything other than very cursory human travel will be possible. No targets are particularly hospitable (Venus especially not, Mars barely), the total land area available in the _entire_ solar system is pretty modest (as usual, xkcd has a visualization: https://xkcd.com/1389/), and the benefits of travel are relatively modest.
My prediction is that we'll likely see more robotic missions, might land humans on Mars (and will likely return them to Earth), but long-duration settlements are relatively low-probability. Perhaps on the Moon. Possibly Mars. Beyond that, doubtful. And they'll likely be little more than research outposts -- I don't think space will prove commercially viable other than for communications (largely Earth-orbiting satellites) and information (again: largely weather forecasting, sensing, GPS, and imaging, mostly aimed at Earth).
As to the bennifits on the long term, aka 100,000+ years. It's less a question of economics but possibility. Can we have an independent space based economy and there is plenty of energy and raw materials so justifying no is difficult.
Our understanding of geology now suggests that a great deal of the heavy and rare elements in the Earth's crust were deposited during the late heavy bombardment -- after the Earth's crust had formed (and hence, after the heavy stuff had sunk toward the Earth's mantel and core), but before there was a lot of life. Which means that a large chunk of the asteroid belt is actually scattered across Earth.
Modulo plate tectonics, previous mining, and other activities.
There are arguments that, e.g., pretty much anything you could want to get is obtainable from seawater, modulo energy (and a significant filtration system).
That said, yes, there are some rare minerals which are useful that might be present in high concentrations in specific asteroids, possibly tracing their own origins to very specific conditions of supernovae explosions which both created those specific atoms and grouped them together.
But moving even a few hundred kg of matter, let alone thousands of kg or tons, is a hugely different proposition. That's a lot of energy to expend, and complexity to support.
My response is "under your feet".
Probably not Alpha Centauri since it's a binary system.
Closer exoplanets aren't necessarily easier to spot, we've spotted those around Gliese 581 because they have a nice short period of a few days.
A close and attentive reader of my original comment might possibly note that my argument wasn't for Gliese but against a. centauri. The salient point being that you'll need to schedule and budget for markedly more than 4.6 light years.