Not sure what you should buy 1st because everyone's needs are a bit different, but I suggest having a diaper game or giveaway at your baby shower. It was a life saver for us! Every guest that brought a pack of diapers (all sizes welcome) were entered into a gift giveaway.
It was wonderful having numerous different sizes on hand for the days you realize your little one needs the next size up.
I would get a carseat (infant or convertible), stroller, crib first as those are larger purchases and are important to have ☺
I kind of collected as I went, but waited until after my baby shower to get a lot. Then If I found good deals I got it. As long as you have the necessities by the time baby gets here you're a okay.