Both my grandfathers died before I was born but my father claimed to have carried a .25 Auto when he drove a truck in the late 1930's. My wife's grandfather, however, definitely had a Colt .25 automatic because it was passed on to me (since I'm the one in the family that likes guns). According to the little blue book it was manufactured around 1916. I suspect it was purchased just before the owner went into the army.
Going back a little further, there were scads of small pocket revolvers around that are almost forgotten today and I would imagine they would have been carried a lot more than the more classic revolvers we associate with that period. The Remington double derringer was still popular then and remained so for decades after the turn of the century.
There were also novelty handguns, if you can call them that, that sold very well at the time, such as the Chicago Palm Protector. There were virtually no laws about carrying firearms and also no laws about product quality, so the market was wide open. Some new fangled firearms appeared and developed a following right away, such as Lugers (in .30 Luger), but it would be a mistake to think that such things were at all common. I would also imagine that most folks had to go unarmed just because they were too poor to afford a firearm. There were a lot more people in difficult circumstances because nobody had the radical idea that everyone had to eat and have a roof over their head.
At least one writer has suggested that, in our grandparent's day, people moved from the country to the city because it was safer and now people do the opposite!
Do you realize that the US Government sold off some of their .45 Single Action Army's as surplus sometime around WWI? I also wondered how long single shot percussion pistols, including Deringers, and percussion revolvers remained in active use after cartridge arms became available? And rifles, too, for that matter.