You can find many alternatives to full view screen doors. These doors are usually installed outside your house, over the existing door frame, and protect them from outside elements. They have also a screened version for warm months.
Wooden storm doors
Wood doors are excellent choices but they some drawbacks. Because of the material, wood doors are more susceptible to temperature changes, humidity and stress, so they will shrink, split, crack, stain.
Although these are important things, they can be treated and you can maintain the nice look of the doors with a little paint and stain.
Metal storm doors
Metal doors are more adaptable. They can be reinforced or better security or made so that they seem self storing doors. Of course that they are very durable and can withstand high damage and they are almost immune to temperature changes. Humidity may cause some problems, but with a little paint you can solve the problem.
Self storing doors
Self storing door usually have sliding glass windows embedded.These can be opened and closed at your choice. You can replace the windows with screens in the warm months.
Security storm doors
These are like typical storm doors, only that they are reinforced for better security. You can also change the windows with screens if you want. The nice thing it that you can play with any fancy design. Metal can form more shapes then wood, and it’s easier to achieve the wanted design.