Keep looking for a good Model 10. The good news is that they aren't expensive so if you buy one and find a better one, it's not much more out of pocket to have a pair!
If you're just looking for a plain shooter, any of the guns made from the 1930's to today will work with standard .38 Special ammo. However, for a defensive gun, look for one marked as a Model 10, up to the time S&W added the lock. These later guns will be able to handle .38 +P ammo.
If possible in your area, don't forget to canvass pawn shops for good deals. Someone may pawn an old .38 they didn't need for the cash. Sometimes these are nearly-new "nightstand" guns that never left the drawer for 30 years.
My favorite is the one below. It's a 5-inch "Pencil Barrel" circa 1970. This one I found in a local shop. All original and like-new with the original box.
For your edification... M&P/Model 10s with serial numbers...
With no prefix: Prior to 1942
"C" prefix - post war 1950's
"D" prefix - 1950's to late 1960's
"K" Prefix - Late 1960's to 1995 (Includes "K" with a leading digit 3Kxxxx)
Three letter prefix - Post 1996
(this is from memory, but sufficient to help you judge the age)