What we are looking for in the perfect exoplanet

Over the last few years, astronomers have found a whole bunch of new worlds, some of which are potentially habitable by alien life, and a few of which may even be habitable by humans.
But what exactly does "habitable" mean? What is it that we’re looking for? The easy thing to say is that we’re looking for a planet exactly like Earth, but really, it’s a complicated question with a much more nuanced answer.
There are two distinct ways of thinking about a potential exoplanet when it comes to life. We can either look at an exoplanet and try to determine whether it’s suitable for colonization by humans, or we can look at an exoplanet and try to determine whether it might be potentially inhabited by aliens. The former, of course, involves a much more stringent set of criteria, while the latter is as boundless as life can possibly get (and we have no idea what that might imply).
For the purposes of this article, we’re going to be looking for an exoplanet that could support human life. And not just technically support human life (in the way that the International Space Station can technically support human life thanks to technology), but actually offer something to potential settlers, such that a colony could take advantage of the planet in some way as opposed to simply surviving there.
Now, all of the criteria for a potentially habitable exoplanet that we’re going to be discussing should not be construed as absolutely necessary, and it’s certainly true that there are lots of special cases (or even not-so-special cases) where a moon orbiting a gas giant (for example) might be a great place for life. However, the hunt for alien life or habitable planets is sort of like playing the lottery, except with the ability to cheat a little bit. There are billions or trillions of stars out there, and we haven’t the faintest idea what the odds really are of finding something that’ll work. All we can do is say, "here’s what we think makes for the best places to start looking" and then look there, and that’s what these criteria are all about: if we were going to send one ship to one alien solar system, here’s the combination of features that we’d be looking for.