Good deal, at least you kinda know what you're looking at. Probably you'll learn much more about the pistol and post your findings here. If possible you may want to have a competent gunsmith give the pistol a good looking over to inspect the re-chambering work done on the pistol, and or if it's safe to shoot 38/200's and/or 38 special.
After WW2 ended, a lot of the 38 S&W M&Ps came back to America. Many of these revolvers were converted after the war, to fire 38 Specials. Some of the conversions were okay at best, where they drilled out the cylinder and replaced the barrel with a marked, 38 Special barrel. But many of these conversions happened as "back room" sort of things, where someone with a bit of machining ability simply bored out the cylinder and left all else alone. There are a lot of these around still.
You can fire low velocity target 38 Special loads through that revolver, and probably be okay, but at your own risk. The factory load for the 38 S&W 158 grain RN bullet only achieved about a 600-650 fps velocity, depending on barrel length, so you want very LOW power loads, and certainly nothing beyond. The .357 diameter bullets of the 38 Special will slightly skid and slide up the .360 barrel that you have on that revolver, never getting a good, sealed contact with the rifling, and you'll get a little gas blow-by, you will never get the kind of accuracy out of it that a factory-made 38 Special M&P will give you. It'll do okay, at short range, but thats about it. I wish I had better news for you, but I do not.
If I were in your shoes, and wanted a 38 Special M&P, I'd be patient first of all, and I'd start looking at the Model 10s on the used shelves. You can still find these revolvers for low prices. Police trade in's are usually a good deal (google Bud's gun shop, and look under used/police trade-in's, they've had them on and off recently for $269 shipped), and they can still be found for under $300. There are shops here in New England that have decent enough Model 10's for $275 to $300 and they will usually take a bit less than their asking prices. A used Model 10 will likely last you your life time, if you feed and care for them as they should be.
Your gun does have some value, maybe you could sell it outright, or part it out, to help you pay for something better.