If you're trying to win, let other people do your killing. Being in the top ten and shooting someone visible means giving away your hiding place, so now everyone else knows where you are. Let someone else do the dirty work; now you have their location and your hiding spot is still safe.
Dropping into contested areas to improve gunskills isn't a bad idea, though, just make sure you're not dropping on top of someone, because the race to get a shotgun isn't as important a skill.
Beyond that, keep your ears peeled, be sneaky, and plan ahead. Almost all circle-related (blue damage or getting killed running by noisely + desperately from the circle) deaths can be avoided by planning and not overlooting.
Vehicles are godlike early and can be a liability later.