Let's start by caliber and assume you truly want something from the pre-80s era.
If you insist on a .357, then there are myriad options to choose from. My favorite are the N frames. The Model 27 and 28 are .357 caliber guns built on a .44 frame. Heavy, with a tapered barrel, available with barrels in 3 1/2, 4, 5, 6 and 8 3/8 inches. The 27 has a nicer polish on the bluing, but internally is the same as the Model 28 Highway Patrolman.
Next step down is the K frames. The Model 19 and 66 are the ones that stick out, but there are other model numbers which are essentially the same frames with different options: barrel type, sights, etc. After some problems with .357 loads with these guns, S&W admonished owners that the K frame should be "carried with .357s and shot with .38s." Many of these problems were later traced back to the hot 125 grain .357 loads that were popular at the time. Flame cutting and forcing cone cracks were the two most common problems.
If you don't mind stepping into the 80s era, you have access to the L frame guns, the 581, 586, 681 and 686. These guns are in between the K and N frame, almost always with a full underlug barrel. Barrel lengths are available from 2 1/2 to 8 3/8 inches. These guns are built like tanks and nice to shoot. Many are available used, since many, many cops in the 80s wound up with the S&W L frames before transitioning to autos.
With some direction and a little time shopping on the internet, any of the abovementioned guns can be found for les than $500, though N frames tend to bring a premium right now.
If you have any other questions, feel free to ask.