I cant speak for 1880 but I have researched crime up to around 1870 using newspaper articles, and thefts of firearms were surprisingly common as was the use of them during crimes by both perpetrators and victims.

The most common guns which came up were 'sporting' guns such as shotguns and rifles, however revolvers and single shot muzzle loading pistols were not uncommon in reports. I have never heard of restrictions on the purchase of any kind of gun at this time, however that isn't something I have ever had cause to research so don't take my word for that.

Some of these reports did mention the value of stolen guns however the precise values were irrelevant to what I was researching so I did not write them down, but I believe one report mentioned a shotgun worth around £2 being stolen.