I used three different types and sizes of screws, some galvanized, some brown deck, and some plain stainless steel. In the end my entire stand including the screws and metal plates I used were all painted over with waterproof sealing primer and then a coat of waterproof paint on top of that
Personally I would be more concerned about sealing the 2x4 wood to make sure they don't absorb water/moisture.
Also, it is a good idea to use wood glue on your DIY stand. The glue will make your stand a lot sturdier than just screws would. The glue also helps to seal cracks in between the wood :-)