long post
@starkatt I'm gonna vote "something else" here, because honestly, the answer that makes the most sense would depend a -lot- on what kind of culture you're dealing with here, and what kind of environmental factors said culture has to deal with in turn. The vernal equinox and the winter solstice are fairly obvious places for temperate-ish climates given that they're right around the time that everything's in bloom and at exactly the darkest time of the year (making it a good "oh shit, we're halfway through the worst part of the year" celebration) respectively, but similarly, I could see a culture in a more poleward place using the summer solstice instead - when everyone can be out and about with no trouble, an excellent time to celebrate life itself.
Autumnal equinox too, given that it tends to coincide with the last harvest before winter.
As for the others, any culture that adheres great significance to the lunar cycle (and there's lots of those, as it turns out) may want the beginning of the new year to coincide with a particular phase of that too (usually a full moon, but there are certainly other possibilities).
Depends on the actual people themselves too of course, if you're straying outside human-equivalent territory altogether. There's no way a land full of werewolves is going to want their New Years celebrations (or indeed, most other holidays) to fall on a new moon of all things. 💙