I am no metallurgy expert, but my understanding is that 316, sometimes called “marine grade” stainless does offer superior corrosion resistance. The “big” Ace a little ways from me offers a nice selection of it, but you can also buy online from places like Marsh Fasteners. It is definitely pricier than 304. There is at least one grill company that offers an all 316 stainless grill. I have bought 316 hardware from both.
Quality 304 stainless is nothing to sneer at, so you might use 316 only on places of highest exposure or difficulty replacing.