The warning first: a V neck will gape the second you lean forward over a desk or down to pick something up, and the deeper the V, the more you'll find yourself doing that small tug at the chest without even noticing. I've caught myself doing it on trains. It's still worth the bother, because almost nothing else does as much for the collarbone and the length of the neck for so little effort, and on the right body it makes the shoulders look a full size narrower than a crew neck ever will.
Fabric matters more here than on most necklines, because anything stiff will hold the V open like a little shelf, while something with drape, a viscose or a softer jersey, will fall closed against the sternum instead of standing proud of it. Over a season of wear that drape is also what ages well or badly. Jersey ones go slightly baggy at the neck edge after a lot of washing, so I turn mine inside out, wash on a cool cycle and never tumble dry, which keeps the binding from stretching out and the point of the V from drooping into something closer to a scoop by August. A woven V neck dress holds its shape for longer but creases if you so much as sit down in it, so it wants hanging rather than folding.
On fit, the depth of the V should sit roughly where your bra line is, not below it, and if there's an inch or two of gap between the two on the hanger, that's the gap you'll be dealing with on your body too, so check before you buy rather than after. Wrap style V necks are the worst offenders for shifting during the day, pulling slightly to one side as you walk, so if you're going for one, look for an actual tie rather than a popper, it holds its position properly. A bigger bust needs either a lower armhole or some structure at the bust seam, otherwise the V widens further than intended and the whole neckline sits wrong by lunchtime.
Underneath, a V neck wants a nude or matching bra, obviously, but it also pairs easily with a slim belt at the natural waist if the dress itself is loose, and with flat boots or low heels rather than anything chunky, which tends to compete with the length the neckline is already giving you.
It suits anyone who wants the top half of an outfit to look considered without having to think about it twice, as long as she's happy to check the gape in a mirror first, not just in a photo.