Flavia commented on this recent Chronicle article about who gets hired where, and when. I have no statistically significant information to impart on this subject; however, I am moved to muddy the waters a bit by introducing some anecdata regarding searches at my new uni, including, especially, the one that resulted in my hiring.
First: I've met a good handful of new faculty at Idyllic State, and none that I know of is right out of grad school; a VAP position seems to be minimal (and there's a contingent of us in the Humanities/Fine Arts who were TT for five years or more prior to moving here). There is one person I've met whom I don't know to have had a previous position, but I don't know that he didn't, either. VAPs and moving from one TT/tenured post to another seems well within the pale, in other words.
Second: It's becoming increasingly clear that, while I'm sure that I wouldn't have been hired if my research hadn't been up to snuff, it's my undergraduate teaching and service experience that clinched my candidacy. Surprise! I genuinely didn't think that my service experience, extensive as it is (and frequently in leadership/chairing positions) would help beyond a certain minimal threshold. As it happens, there is a Service Gap in my new department, and also increasing pressure to grow undergraduate enrollments. My strengths, unexpectedly, were a fit for their needs.
Thus, my teaching award, years of positive evaluations with a 4/4 load, chairing of the curriculum committee and subsequently the division, and directing the Honors Program (which involved recruiting and considerable encouraging of students) made me a particularly attractive candidate. Presumably the fact that I continued to publish during this time helped, of course, but it's been pointed out to me since I got here that I have a lot to offer in terms of undergraduate education and outreach. I honestly didn't think that that would matter so much at what is a decidedly research-oriented university.
So...you never know. My research portfolio, on a more junior candidate, might have been much less appealing to the search committee (not that I know that, of course). The things that I emphasized on my CV because, well, why not? happened to respond to needs within my new department that I could not possibly have anticipated.
Good luck to everyone who's on the market. It sucks, truly. And "fit" is a real thing, even if it means a lot of different things; you really can't judge what a committee might be looking for, beyond, of course, what's on the job ad. (And there's always stuff beyond the job ad.) The only (rather lame) bit of advice that I can give is to 1) clearly note on your cover letter how you are the best possible fit for what the committee is asking for; 2) explain yourself if you're moving from a t-t or tenured position; and 3) play up anything (within reason) that may help you stand out.