I'd think an electric car would be best for this work, as long as the batteries have the range required. Factor in the range reduction that might occur on hottest & coldest days.
I have a manual Cruze, no auto-stop. I test-drove an automatic, and wasn't put off by the auto-stop. Some people have posted work-arounds for when you don't want the engine to shut off. I wouldn't put it on the list of cars good for a delivery route, though. For a 200 paper delivery route, I'd go for an even smaller used car, or an electric car.
Had an over 100 newspaper route for six years when I was dumped on this planet, 24/7, when weather was permitting, used my bicycle, when not, walked. Sunday was the worst with over a hundred Chicago Tribunes. All the money went to my mom when my dad took off, no such thing as welfare back then.
Today I see old clunkers delivering newspapers, would think their automotive cost would exceed their profits. UPS and Fedex trucks are always driving by, have to kill their engines when stopped, wonder how long their starters last.
Use to set the papers behind the storm doors, made my customers happy, made more with tips than delivering the newspapers. Quit that route when I turned 16, could earn a lot more money by setting pins at a bowling alley, and the weather was not so harsh. This job was killed by automation. Did that until I was 18, then I was drafted.
Can you really make a profit driving a brand new vehicle delivering stuff?