I've been thinking/searching about similar things, and started looking at it from matters of weight/size vs cartridge/ballistics/capacity.
The 158gr L-SWCHP .38 SPL +P with 890fps and 287 ft/lbs is a popular SD round, even in .357s, because it's manageable and effective. I think it's Winchester X38SPD, nothing exotic or real expensive.
The cartridges need a container. Many S&W 15 oz Airweight J frames (642, 442, 637, etc) are rated for +P, and should work with that 158 +P cartridge.
Charter Arms also has a bunch of 16 oz 5-shot +P rated guns, and also have the Undercover Lite at 12 oz (which most think is too light for the cartridge). If you'd feel better with 6 rounds they have a .38 Police Undercover, which is a +P rated six-shooter, but it's built on the Bulldog frame so it's a little larger than the Undercovers, and weighs about 4 oz more, making it a 20 oz 6-shot .38 +P.
I think most of those guns can be found for around $400.
Older lightweight guns with 3" barrels are among my favorites, but limited to non +P ammo, like the S&W M37 and the 3" Undercover.
I sort of have the hots for the new Charter Arms Pitbull .45 ACP, but it's built on a new frame which I've read is 2mm larger than the Bulldog frame, and weighs 22 oz. More size and weight, but it's a .45. Decisions, decisions.