Paint is not a good choice for a deck, paint is not meant to be walked on. I would power wash and go with a solid stain instead of paint. which can be applied with a brush, sprayer or roller.
Does your deck have failing paint on it now? If so a wash, scrape and prime might be needed. Primer is not necessary under normal circumstances for a solid stain but it might be if paint was used before depending on condition of the deck. You have any pics?