The 581 is essentially the fixed-sight version of the 586 - the corresponding guns in stainless would be the 681 and 686. These guns were built on the S&W "L" frame, which is a bit beefier than the K frame but uses the same size grips. There are those who object to the full lug barrel, but personally I like the look, which is reminiscent of the Colt Python. I think most would agree that they are among the finest .357 revolvers made. I have a couple of the 686s, and a few 586s, and they are all very accurate and fun to shoot.
The no dash and -1 guns in this series were subject to a recall to fix an issue with the firing pin and bushing that could [very rarely] result in the cylinder locking up due to the primer cup flowing back in to that area with certain hot loads. Guns that have been modified by the factory will have an "M" overstamped in the frame cutout near the model number. I believe S&W will still make this modification at no cost and will cover shipping both ways. If the gun in question is to be used for SD, than you will want to be sure the modification has been, or will be, done. For range work it probably doesn't really matter.
With the current craziness in gun and ammo pricing generally, it's difficult to judge what would be a fair price. Based on your description and the general run up in quality revolver prices, I think that something in the $550 to $600 range is reasonable, but it's a seller's market these days and I see desirable guns bringing prices that would have been unthinkable just last year. I think on balance the 586 and 686 adjustable sight models are more marketable, but there were also a lot more of them made, so for those who like a fixed-sight revolver the 581 and 681 are harder to find and scarcity always carries a premium.
If I came across a 581 in good condition I suspect I'd be smitten and well and would likely pay top dollar to take it home.
. I would appreciate any insight that you may have.
