tdballew - you had your model correctly named. The 32 Single Action was manufactured from 1878 to 1892, with almost 98,000 sold. Your revolver was probably shipped from the factory around 1880. These guns seem to be built well enough to use the modern 32 S&W cartridges, but there is always the chance that any gun over 130 years old can break a part. Some parts for these revolvers are very difficult to find today.
I always see the comment that the gun should be checked out by gunsmiths before shooting. If the owner is a knowledgeable gun enthusiast, they should know the same things to look for that a gunsmith would check. I doubt that many gunsmiths will have the equipment to look for micro-cracks and will probably tell all owners of black powder guns that they should not be shot with smokeless powder or just say don't shoot them at all. Tight actions, proper function, positive cylinder lock-up, solid hammer/trigger lock-up, good bore, etc. are about all there is to look for.
The 1905 M&P Fourth Change was manufactured from 1915 to 1942, with over 500,000 made. They are great shooters and lots of fun to shoot. No high pressure loads, but standard 38 Special ammunition is fine.