S&W 4th .38 DA
I have one just like it, but with the original black hard rubber grips, and the finish on mine is more complete. .38 S&W ammo may or may not be difficult to find depending upon where you live. You won't find any at Wal-Mart. It is still made, so you may have a good local gun shop that has some in stock, or could order it for you from their jobber. You are not likely to find anything other than 145 grain lead bullet loads. If there are any halfway decent gun shows in your area, .38 S&W usually can be found there. Newly-manufactured ammo is perfectly OK to shoot in your 4th Model, assuming it is tight and in good condition. I reload all my ammunition (.38 S&W included), but if you are not a reloader, that's not much help. You probably won't want to shoot the .38 DA much, as it's not what I consider comfortable to shoot due to the very small grips. I shoot mine very little for that reason, but I have other, and better, shooters in that caliber as well. I think the Pre-1899 cutoff manufacture serial number is around 382,000, but I do not remember exactly. Anyway, yours is definitely pre-1899, so it's not considered a firearm by BATF regulations. Mine is slightly newer, with a SN around 366,000.