A storm door usually gets put off until the first cold week, and then the gap under the old door shows you why it mattered. The installation itself is not complicated, but it goes better when you settle a few decisions in the right order.
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Before the order goes in
Measure the opening yourself rather than trusting the old door or your memory. Take the width at the top, middle, and bottom, and the height on both sides. If the widths do not match, the frame is out of square, and the installer needs to know before the door is ordered, not when the box arrives.
Decide the swing and the handle side while you are standing inside, facing the outside door. Say it out loud, then write it on the order. A door built the wrong way takes the most time to fix, because it has to be ordered again.
Pick the style based on how he uses the door. If he goes out to the porch or the mailbox in every kind of weather, a retractable screen may matter more than a full glass panel, because it is quicker to open and close without a fuss.
On installation day
Ask what happens to the old door and frame. Find out whether they are removed and taken away, or left for you to deal with. Ask whether the crew will check the sill and threshold for gaps and soft wood. If the sill is rotting or the frame moves when pushed, a storm door cannot sit right on it, so ask for that to be named as a separate repair before work starts.
Watch the closer and the latch being set. Ask them to open the door fully, let it go, and see whether it closes slowly and catches the latch without slamming. Ask them to show you how the closer tension adjusts. You will likely change that setting at some point, and it is easier to learn it on the day than from a booklet.
Check the clearance. Look at the porch rail, the doormat, and any outside light or vent the door might hit. Open it all the way by hand and watch the edge.
The walk-through before you sign
Before the crew leaves, have them walk the door with you from both sides: open, let go, watch it close, and check the latch from inside and out. Ask for the model number and the paperwork, and put the warranty card in the drawer where the other house papers live. Do not sign the completion sheet until you have watched the door close on its own several times, because that is the moment you can still ask for an adjustment while the crew is still there.