I'm not as expert on long products as on flat, but 303 with all its elongated sulfides may present some problems with splitting. Why not use a low sulfur grade which would also have better corrosion resistance?
In general you pick the stainless grade which resists the given environment and doesn't need coating.
I concur with McGuire’s comment about potential splitting of 303. Also I am not sure there would be any reason to use free machining S.S. except for a machining application especially since EdStainless is pointing to the standard S.S. for rivets.
Passivation is one of the most common surface treatments for enhancing corrosion resistance of S.S. but I would be most interested in hearing suggestions by others for your particular application. Please elucidate with respect to environment.