brush, then go for it. it’s a matter of preference. personally i place the lid until the sugar is dissolved.
i stir lightly the sugar to make sure everything is dissolved completely. but don’t do this for too long and don’t stir like crazy. all you want is to make sure that the areas where the pot gets less heat are dissolved. this brings me to another point that i have to mention. make sure the pot you use gets even heat from your stove.
you can see above the sugar is melted already and the center of the pot is boiling more than the outsides. i take my spatula and kind 