From having sewn other garments, I would expect to sew the shoulders together first, then collar to the neck epening, and last, the side seams.

Beyond that, the finishing depends on garment. For a down-filled vest, you may be able to get away with quilting-through the vest. I have never worked with down, so can't give advice on that. If you are using a poly-fill, you may get away with sewing 3 vests: inner, batting, outer, wth seams to the inside. I haven't done this either except for mittens and cozies.

What is going on with the collar?