I have a vertical roller screen at home. It has upper and lower tracks, secures by a magnet when open. It does its job when open but leaves and dirt get caught in the lower track and require frequent vacuuming. The top track has a runner that needs WD-40 to slide easily. The top screen tears easily if I pull too hard against the dirt. Do not know how salt would affect this. Took the dog two days to learn to open it by pushing with her nose.
When Fanfare was new my Dad had the Richard Bertram yard to make a set of teak aft screen doors. Apparently he did not ask for a bid as the bill was about $1,000 which he felt was excessive (then!). They are still working well. They fold in, paralleling the AC/entertainment console on one side and the wet bar on the other so really don't take up much extra room. Closed, you won't notice.
No screens on the helm doors. Mostly we leave everything open except when cooking to keep the flies out. Don't seem to be many mosquitos these days. Key West at dusk has flying termites, close for that (important!!) No-seeums in the Bahamas require everything shut, AC on.