If you are going to put up a storm door for energy saving purposes of for aesthetic purposes there are some things to consider either way:

For one, never add a glass storm door if the door gets more than a few hours of direct sun each day. The glass will trap too much heat against the entry door and possibly damage it. And, if your purpose is to make your door more energy efficient you may just do the opposite.

Storm doors for patio doors are hard to find but they are available. Adding one to a modern multi-glazed energy-efficient low-e door is not a great idea, and is seldom economical as the patio door is already as efficient as it will likely be, and since patio storm doors are rare, the cost to do so would be great. A better option for making a patio door more efficient would be to add insulated drapes; these will make the room much more comfortable when closed for the night in the winter (or on sunny days in the summer).

If you are going to purchase a storm door, make sure it is a quality door. High quality storm doors use low-e glass. Frames are usually made of aluminum, steel, fiberglass, or wood (painted or not).

If you are looking for something that is low maintenance, do not go with a wood storm door. Wooden storm doors require more maintenance than the other types as the paint is more likely to peel faster, and weather affects them more. Metal is your best option. Metal-framed storm doors and windows can be highly energy efficient as they generally have foam insulation in their frames.

Storm doors differ, and so don't fool yourself into thinking that one storm door is just as good as another. Some doors have self-storing pockets for the glass in summer, and an insect screen for the winter.

When you put in a storm door make sure you use a high quality weather stripping. When selecting weather stripping, you should consider the durability of the material as well as what type of weather stripping works best for the type of storm door you are installing. Different types of weather stripping are better for different types of projects. Bent metal weather stripping is also one of the most expensive weather stripping materials. Bent plastics are similar to the bent metals, but are less expensive. They are also less durable. Most rubber and foam materials stay flexible for years, are inexpensive, easily replaced and effectively seal air leaks, and is probably the best choice for weather stripping storm doors. You should choose the appropriate door sweeps and thresholds for the bottom of the storm doors as well. You want to make sure that the weather stripping around your storm doors in installed properly and can withstand harsh weather conditions. If not, the storm door is just going to be something to look at, not to protect or add efficiency.