What size do you want the gun to be? An N-frame S&W, Model 27 or 28, will be able to shoot all the .38s and .357s you could want. It is a large gun, but they are fantastic shooters. A used Model 28 in good shape should be somewhere over $400. A Model 27 will be more.
If you are looking for something a little smaller, then you should probably look at an L-frame. It will be a bit difficult to find an L-frame that is pinned and recessed since the L came around in 1980 and pinning/recessing stopped shortly thereafter. However, Models 581, 586, 681, and 686 are fine guns and make fantastic shooters. The L-frame is a little bit stouter version of the K-frame, which just couldn't stand up to consistent full-house magnum loads. However, Models 13, 19, 65, and 66 are fantastic revolvers built on the K-frame; just might not be what you are looking for. These are all commonly available for $400 or less.
As for anything smaller, a vintage J-frame is not going to be up to the task of .357 magnums. S&W has a new Model 60 built on the J-magnum frame with a 3" barrel that is a nice little bugger; but it costs over $550 new.
If it were me, I would be looking for a good used Model 27 or 28. However, I am not a big .357-full-house kind of guy, so I am also not against owning the K-frame Models 13, 19, 65, and 66. Just a matter of choice.