You basically have three main choices. A used Smith and Wesson J-Frame or a Ruger SP101 or a Ruger LCR.
I'd head to your local gun store and see what they have.
Yes, you can shoot any .38 special ammo out of a .357 revolver, including +p. In fact, most people I know who carry revolvers carry .38 +p in a .357 revolver. Shooting actual .357 out of a small gun is really unpleasant and for most people doesn't make sense. That being said, .357 revolvers are strong enough to handle a lot of shooting, so it still makes sense to get one.
There are about a million different j-frame variations out there. Get what works for you. Most j-frames have 2" barrels, although some have 3". You shouldn't have too much trouble having finding something in your price range. Look for a used model 60, a model 640, a model 360.
There are just a few different version of the SP101, different sights and hammers. They pretty much all have a 2 1/2 inch barrel. A new or good condition SP101 will be close to $500, but you may be able to find one that's "shooter grade" or your price.
The LCR is a polymer-framed small revolver. It's cool, too, but it's the type of gun people either love or hate. It's worth noting that Smith and Wesson makes a polymer-framed revolver called the Bodyguard, but it's a really similar style to their metal j-frames.
Good luck with the hunt. Other's on here might mention Charter Arms or Taurus. I don't have any experience with them, but they do not have the same reputation for quality and strength that Smith or Ruger have. They are options, but you won't go wrong with two major brands.