If it is an S&W M&P model, that s/n would date to somewhere about 1924 to 1927 I believe.
Installing a new barrel on an S&W hand ejector type revolver is not a small job. It takes machining equipment as well as knowledge and skill. If the gun is in otherwise excellent condition, it might make sense to try to find a period correct barrel (pre-1930; there was a small design change about then) and have a gunsmith install it if you have one locally who can do it for a modest price (probably about an hour or a little more of shop/bench time would be the charge). So if you are patient and spend time connecting all the dots, you could perhaps get it done for $150, and the gun would be worth perhaps $250 assuming it's otherwise nice with the correct grips. The barrels were s/n to the gun, so it will always be obvious it was re-barreled. If you do not have the patience to do all that, then parting it out or selling it to a gunsmith or old collector like me is a better bet.