I'm asking mostly in the context of living Latin and trying to figure out how to say things like "I decided," "I started a blog," "I set up an organization," "I instituted a policy," and so on, for all of which some version of statuó seems appropriate.
Excerpted from Döderlein's Handbook of Latin Synonymes:
Instituere; Instaurare; Restituere; Restaurare. Instituere means to establish a profane, instaurare, a sacred, or honorable, or generally important institution, such as sacrifices, sacred games, wars and battles. Hence is instituere itself a usual, instaurare, a solemn, select expression. In the same manner restituere is distinguished from restaurare.
Destinare; Obstinare; Decernere; Statuere; Constituere. 1. Destinare and obstinare denote forming a resolution as a psychological, whereas decernere and statuere as a political, act. 2. Destinare means to form a decided resolution, by which a thing is set at rest; obstinare, to form an unalterable resolution, whereby a man perseveres with obstinacy and doggedness. 3. Decernere denotes the final result of a formal consultation, or, at least, of a deliberation approaching the nature and seriousness of a collegial discussion; statuere, to settle the termination of an uncertain state, and constituere is the word employed, if the subject or object of the transaction is a multitude. Cic. Fr. Tull. Hoc judicium sic expectatur, ut non unæ rei statui, sed omnibus constitui putetur.
I've also heard condere in reference to organizations and websites, e.g. Nuperrime situm/sedem ad linguam Latinam pertinentem aliquot homines in rete universali condiderunt.