I would keep the original finish.
It's actually a Police Positive Special, as the cylinder is longer for the 32-20 and 38 special cartridge, and I have never seen a target PPS in 32-20.
Yours is the nice fixed sight model.
Does anyone know of any grips that fit these guns, because I think the grip frame size was discontinued some time in the mid twenties, and consequently, aftermarket grips were usually only
made for the later models in 38 spl.?
Ammo is available, at least occasionally, from Winchester, Remington, Ultramax, Black Hills, Ten-X, HSM, Load-X, Buffalo Arms, Wisconsin Cartridge, and others.
Most of it is all lead, thought sometimes someone will make a run of JSP.
There are even dummy cartridges available from AZOOM.
If you want to spend the bucks, (I think about $75, which is expensive), you can get a letter in a couple months from Colt, telling you a little bit about the gun, and where it originally went.
Most seem to have gone to hardware stores, or department stores.