M&P 22 or SR22 are both inferior to the Mk III or 22/45 for what you have described you want to do. Shoot steel.
For shooting steel you want a tune-able, reasonably light, short, fast trigger. So while I'd not say that what I'm about to show is "the best", its a far sight better than what you could do with any low end da/sa style gun. A CZ75 in .22 might be another story, but that hasn't been brought up.
This is my Mk II. I got it for my 18th birthday, back in late 80s. Its a 6 7/8 "Government" bull barrel gun with a japanese dot sight from the same era. It still works great. This gun has an early 90s Volqhartson trigger kit in it that includes a wide trigger, sear, and hammer. It is awesome on steel. The weight keeps the dot sight on target from shot to shot. It is a bit slow to index because of the weight.
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Then last year, I got an idea. Why not build a compensated pistol that is also light. The comp will keep recoil down and the weight will help speed up transitions.
I ended up with this. Its a 22/45 Lite with a Miculek comp, a Power Custom trigger kit, a mag safety delete bushing, and a Bushnell TRS-25 dot sight. I love this gun. It runs great, and recoils less than the 25 year old Mk II even though it weighs half as much. Its not the prettiest thing, but it works. Shooters who do much better than I do have tried this gun and all have been amazed at how good it is. There's about $650 in it.
