Much depends upon the shooter's hand size, which affects the choice of acceptable grip size range. I have skinny fingers, so I can get my middle, ring, and pinkie fingers firmly onto the OEM grip of an SP101. A 3.1" SP101 could serve quite well as a go-everywhere handgun, as could longer-barreled SP101 variants. The only defensive/tactical liabilities of the small-framed SP101 is five instead of six rounds in the cylinder, and less clearance for speed-loading. The grip material can be sculpted for more clearance, but the fact remains that larger-framed revolvers have more clearance for speed-loading. In addition, I would rather not remove any surface area from the tiny grip, as every bit of the surface area of its rounded contours mitigates recoil. When I have carried an SP101 as "primary," I have usually carried a second, and sometimes a third.
Two of my .357 SP101 revolvers were customized by Jack Weigand, back when he still did custom 'smithing. The other two have no custom work, and no aftermarket springs, yet I shoot them just as well. I selected them for smooth actions, new, out-of-the-box. Ruger can make a smooth DA action, indeed.
The GP100 may fit into the stated budget. I would not feel under-gunned if I still carried a GP100 in my police duty rig, on the sometimes-mean streets of Houston. (Admittedly, the usual back-up handgun and Benelli M2 would be part of the equation.)
S&W has good options, too, but well-preserved samples may be above the stated budget.