Start then drop. Probably makes no difference. If I had to manually drop I'd probably drop first, though. With a cue arm the drop is slow, steady, and straight every time.
I'm manual drop, so I might switch to drop first. I always spun first, but then saw someone do it the other way! I tended to find that my stylus would often slam across the run in really quickly as well.
I have a couple edge warped albums that play fine if I place the needle then start, but I usually start then drop, mainly because it's more satisfying that way.