N.b. standard I Am Not A Lawyer caveats.
Based on what little I've read, particularly re: Terms of Use/Service, the answer to Do we incorporate as an official organization? is almost certainly Yes. The questions isn't really Whether we do, but How to do it.
What kind of organization? Again, based on a bit of internet research, our options (in the US) appear to be to incorporate either as a Limited Liability Corporation (LLC) or as a non-profit. Now, "non-profit" is not the same as "tax-exempt"— federal and state tax exemptions are applied for separately, after the non-profit has been officially created. I have no idea if there are any advantages to being a non-profit without having tax-exempt status, or how feasible us getting tax-exempt status would be. It would also depend on where we decide to incorporate, since requirements differ from state to state. Speaking of.
Where will we incorporate? Delaware seems to be a popular choice, for its extensive body of corporate law, its efficient corporate litigation apparatus (the Court of Chancery), and its "pro-business environment". However, we may not ever reach the scale where we would enjoy many of those advantages (then again, who'd have thought four years ago we'd be talking about incorporating?), though again that's speculation on my part. In any case, if not Delaware, than the home state of one of the admins, I would imagine. No idea what if any advantages could be gained from incorporating outside the US.
Who will be in charge? Admins, I reckon— see below.
What will our structure be? Both the LLC and the non-profit appear to require a Board of Directors or some equivalent, so I would expect that the Board would be made up of all active Admins. Also note that who runs the corporation is not necessarily the same as who owns it (yet another consideration). Beyond the Board though… I dunno, but we'd have to figure that out also. There are a bunch of documents that would need to be written, include articles of incorporation, a corporate charter, and a set of by-laws, in addition to the terms of use.
Hmm. Let me rephrase: there's a shitload of documentation that's gonna have to be written.
How will we finance this? Once we have an idea of how much money we'll need (initially and ongoing), we can start a proper donation drive, one with goals and running totals and transparency. We can't really look to the last donation drive as a predictor— assuming we spell out exactly what we're trying to fund. Also "official" merchandise sales, whenever those can be up and running (though I have no idea if that should wait till after incorporation).
Personally, I'm leaning toward seeing if we can make it a non-profit, pending more info, of course.