This has always been a “irk” point with me and my husband. I say dust first and then vacuum. He says vacuum first because it causes dust. But then you would have to vacuum again after dusting. Which would kick up more dirt and dust. So you would have to dust again. And on and on.
We have a central vacuum system in my apartment (holes in the wall with suction) which means no dust will be kicked around with the air blower in the normal vacuum cleaner. Thus dusting first from top to bottom then vacuuming makes it clean at home for me!