Adding a storm door can be a good investment if your existing door is old but still in good condition. However, adding a storm door to a newer, insulated door is not generally worth the expense since you won't save much more energy.
Storm door frames are usually made of aluminum, steel, fiberglass, or wood (painted or not). Wooden storm doors require more maintenance than the other types. Metal-framed storm doors might have foam insulation within their frames.
High-quality storm doors use low-emissivity glass or glazing. Some doors have self-storing pockets for the glass in summer, and an insect screen for the winter. Some have fixed, full length screens and glass panels that slide out of the way for ventilation. Others are half screen and half glass, which slide past each other. Some are removable for cleaning, others are not. All of these features add some convenience and higher costs.
Never add a glass storm door if the exterior 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.
Storm doors for patio doors are hard to find but they are available. Adding one to a new, multi-glazed, low-E door is seldom economic. Insulated drapes, when closed for the night in the winter (or on sunny days in the summer) are also a good idea.