Hi,
First off, you bought in my opinion the finest all around revolver S&W ever made. One of the best "out of the box" double action triggers that I have ever used. I have three K frame magnums. A model 13, 19 and a 66. The reason, all three are among my best shooters.
Now for ammo.
Your model 19 should be able to handle any factory 38 special ammo including +P. The model 19 was designed to handle 357 magnum pressures, so using 38 specials at there lower pressures won't hurt the revolver. Personally, I shoot mostly target 158gr 38 specials.
As far as 357 magnums rounds. If you want to shoot 357 magnums stay with the heavier 140 to 158 gr rounds. For practice at the range I use a lot of the CCI blazer 158 gr hollow points. This round is a mid power round that won't hurt a model 19. I have used this round in all of my K frame magnums.
As for a self defense round. I would suggest staying with a quality 38 +P round like the proven "FBI" round made buy either Remington, Winchester and Buffalo Bore. They have a good track record and at one time were the choice of most LE agencies.
For most people, using the 357 magnum is not the best option. Recoil, blast and follow up shots are harder plus indoor use is harder on hearing.
I would start shooting at the range 38 special 158 gr rounds and then once you get used to your revolver then try the 357 magnum round.
Good luck,
Howard