The recent developments on the consistency of NF bring welcome closure to the longstanding open question about whether NF was consistent. And this is naturally a very important matter for those who find NF set theory attractive.
To my way of thinking, however, NF was never competitive in providing an attractive account of set theory, and the consistency question doesn't really change this. From my perspective, NF set theory is not based on expressing the fundamental truths of a coherent conception of the nature of set, as in the case of Zermelo's theory, but rather arises by a formal limitation of the axioms of an earlier naive (and easily-proved wrong) set theory so as to avoid a known proof of inconsistency.
I see NF as arising by a process of formal manipulation of the axioms, rather than a mathematical idea, and in my view this is not a sound method of finding robust meaningful principles in the foundations of mathematics. One doesn't reliably arrive at important or even interesting principles of set theory by fiddling with formal details like that.
The NF consistency question was open so long in large part because nobody had a coherent idea of what the theory was supposed to be about. There was little reason to think it was consistent or inconsistent, and the fact that it turns out to be consistent is something like a lucky accident. Perhaps the consistency proof will provide a picture of how we can conceive of the NF conception of sets, but I find this backwards and I believe that it will have little to do with our ideas about sets. NF is about something else.
Some philosophers of set theory sometimes express the view that the (inconsistent) general comprehension principle expresses something important, and they regret that it was shown inconsistent by Russell, seeking instead to save it somehow. This is what NF aims at, to save general comprehension as much as possible. This is also what motivates paraconsistent set theory.
My view, however, is that the general comprehension principle is simply a logical fallacy, one that is very easily shown to be false. It has a one-line refutation. It is wrong, and trivially so, and there is nothing there that needs to be saved. In this sense, general comprehension is something like denying the antecedant—anantecedent—an intuitively plausible principle for those who consider it naively, but ultimately it is shown wrong as a logical principle for trivial reasons. We don't mount huge foundational efforts to "save" the principle of denying the antecedent, and I see little reason to mount similar efforts to save the similar easily-proved-wrong principle of general comprehension, including the versions of it in NF.
Meanwhile, the Zermelo theory does express the expected fundamental truths of an understanding of sets arising in a transfinite cumulative hierarchy. The axioms are amply justified by the picture of sets arising in a vast cumulative hierarchy, where we may begin with some urelements, or none since they are not actually need for any purpose, and then form sets of them, and sets of these sets, and so on transfinitely. This picture of the set-theoretic universe leads easily to the Zermelo-Fraenkel theory, while incidently providing no support whatsoever for the general comprehension principle (although it does support the separation axiom, denied by NF). Also, it provides no support for the kind of sets that you describe outside the well-founded framework.
So I am inclined to take ZFC as expressing the fundamental truths of our understanding of sets as they arise in the cumulative universe of sets.