I voted Ruger. I've got a Mk. II (nearly the same as your Mk. III) and a Buck Mark Camper URX.
The Ruger's easier to take down; it doesn't need the sight rail removed with an allen wrench to field strip it. It was also more reliable and less ammo-picky out of the box than the Browning has been. It will shoot even the cheapest bulk stuff reliably until it is so gunked up I can hardly believe it.
The Ruger's disassembly, when it is new, requires that that barrel receiver assembly be tapped off the fram with a mallet. But it loosens up quickly, and after that, all you need is the tip of a screwdriver (or even a spent case) to pry up the edge of the disassembly lever.
Throughout all this, the sights stay aligned, as they are integral with the receiver/barrel assembly.
If you want a little less of the liability-concious junk, you might seek out a used Mk. II. Better triggers from the box, because they don't have the magazine disconnect. The mag release is at the bottom of the magazine, instead of behind the trigger loop, but it is not a combat gun, so you will probably be OK with this. No loaded chamber indicator, and less warning stamped into the side of the gun. You can probably score one for $250 or under. I think I paid $250 for mine, lightly used, in 1997. It is still going strong thousands of rounds later.
