Have you considered Taurus? They are about half the price of a S&W and from what I have seen the same quality or better. I have never known of a Taurus to misfire. I know they are made in Brazil but S&W has cut American gun consumers throats so many times that I would rather buy Chinese guns than support those wretches.
Personally I would get an Air-weight hammerless in the Taurus, for the money and the feel it can’t be beat. Pick one up someday and you will see.
One advantage of the 357 is you can plink with cheap 38’s while 44 special ammo costs more than 44 magnum ammo (at least here).
Taurus 605, 357 Mag ($375.00)
S&W 637, 38 SPL ($425.00)