The process you outlined is correct. In terms of what to use to keep that most away, consider Spray and Forget. It's very effective in cleaning moss growth.
And once you eliminate that moss, be sure to sand the surface well to remove any loose paint, and then apply a good oil-based primer. Once the primer dries, apply a good oil-based exterior floor paint. The reason I recommend oil-based is adhesion and durability. Latex-based finishes are great for walls and ceilings, but in my experience, they don't have the durability necessary for keeping floor paint in place - especially on moist surfaces like wood.
It sounds like you've got this project under control. Good luck!