38 Special is an old, low pressure rounds from the early days of smokeless powder. 357 Magnum is an evolution of 38 Special that came about by increasing the pressure limit significantly, which allows for significantly higher velocities. 357 Magnum cases are a bit longer than 38 specials-with some bullet profiles this allows a slightly higher powder capacity(and not with other bullets like the Ketih type 168gr LSWC), but more importantly the longer case keeps the cartridge from chambering in 38 special guns. A 38 Special will chamber in a 357 Magnum gun, but not the other way around.
In any case, it's hard to go wrong with the model 64. It's the stainless steel version of the Model 10, which in turn is an evolution of the S&W M&P Revolver. The lockwork/overall design is basically identical to that used in the S&W Model of 1902, and the frame size and construction dates back to the Model of 1899. It's a time tested and proven design. The fixed signs aren't the easiest in the world to see, but you don't have to worry about them getting knocked out of adjustment and they draw from the holster easily.
For a while, I had an ex-prison-guard Model 64 basically identical to the one pictured(4" heavy barrel, AKA "bull barrel") aside from it being factory double action only. I stupidly sold it. Mine was beat up from being carried a lot, but hadn't been shot much. It was a great shooter, and with standard pressure 38 Specials is a very soft shooting gun. It will handle 38 Special +Ps, and is more than manageable with those.
IMO, this sort of gun is a much better choice for most people than the now popular 2" snub nose revolver. These are easier to shoot and recoil less. They're not AS easy to conceal, but are still doable, and I did carry my 64 that way some.
As for a JHP-one of my favorite loads for this gun is the Speer Gold Dot 135gr +P "Short Barrel." Despite the short barrel labeling, this is a load that actually performs really well in a 4" barrel. In fact, I've been told-but can't verify it-that it was developed for the NYPD primarily for their Model 10/Model 64 Duty Revolvers, but also performed well in the off-duty snubs. With that said, I rarely carry a JHP in 38 Special, and have instead settled on the 158gr +P LSWCHP, AKA the "FBI Load." In proper form, this is a soft lead semi-wadcutter hollowpoint that expands nicely even at 38 special velocities. Even if it doesn't expand, it still acts like a semi-wadcutter, which has somewhat better terminal performance than a round nose.