I bought tack before I owned a horse: grooming tools, saddle pads, horse size halter, leadrope, etc.
Stirrup leathers and irons are convenient so you don’t have to constantly shorten/lengthen. When I was in lessons or even leasing, I rode mostly smaller horses (15h - 16h) and a 48" girth fit most everything.
I agree, buying a bridle would be hard - too much adjusting to get it to fit each individual horse and swapping bits. If you do end up buying bit(s), 5" is fairly standard, and it doesn’t hurt to start a little collection of various snaffles.