In undergrad I had two second-author publications, was graduating summa cum laude, awesome letters of rec, a member of every club, honors society, etc, on campus, was a part of a federally-funded research program for low-income first-gen students, as well as participating in four labs- two of which I was in for 1+ years and had awesome relationships with the advisors. I applied to 18 programs and was rejected from almost everywhere, the ones I was accepted to I realized I didn't want to attend... at all. And I think that was the issue applying out of undergrad, I had barely turned 21. I knew I loved research, suicide, and adolescence/emerging adulthood, but I didn't know much else. And it definitely showed in the schools I applied to- no concern for research fit. My GRE score also sucked.
So since I was fairly strong in all other aspects, I'd say that fit with a particular professor/mission statement of the university is important, as well as your GRE scores.
That was also the feedback I got from the schools I was rejected from 😉
I took some time getting a (funded, woohoo!) M.A., took the GRE again, and was able to pinpoint something I love doing, and immediately was accepted into my top-choice doctoral program. Looking back, I think the research fit and personality fit was most important. My current advisor does work on literally exactly what my thesis is about.