Of your specific choices, though normally averse to "just" 5 shotters, I selected SP101 for the reasons others have mentioned. I'd shoot +P .38s as a regular/HD diet, advancing to .357 for serious "social" duty and trekking (mountain lion, drugged 2 legged varmints etc).
Alternate choices: Same SP in new(ish) six shot .327 Fed Magnum.- as something different and certainly interesting. Regularly shoot H&Rs as the .327's "special" equivalent. Early reported teething problems and ammo/components slow to the market a detractor, but here for the long haul I think and a perfect match of cartridge and platform IMO.
Also, a Rossi 461/462 .357 snub--6 shots in a similar size to SP (J+/Detective Special/D-frame(ish), with far more good reports coming in vs bad, including a recent, surprising report on one of these or other forums of moderate recoil even with 125 gr .357 . Must be the grips--and, like the SPs, steel construction doesn't hurt either. Like any of this type snub, I'd shoot mostly .38s/+Ps in it anyway to prolong gun life and keep the obnoxious level down, but nice to know you can "go magnum" if needed. These are a real buy. (you'll hear a lot of kneejerk negatives about Rossis, 15% (maybe) of them with *actual* modern-Day Rossi experience),
Also, a nice used pre-lock K 3" .357 (65 or 66)--my choice, 65LS ("Lady Smith") as the best of the bunch IMO. This is up there near, at or beyond your $ limit. But, they're a real gem. Like all Ks, regular diet should be limited to 158s vs 125s.