This is wonderful feedback, thank you. I think I will probably go with cats, then. I am not worried about them getting the ducklings--I have to protect babies from all kinds of things already--hawks and owls and foxes and domestic dogs and so on, so I'll just add domestic cats to that list. I am a little sad about the prospect of them eating the local snakes, though--if I could get someone to drop a couple black snakes in my backyard to control the mice, I'd be glad of that too. I wouldn't have to pay vet costs on snakes, lol!
On the other hand, we do sometimes get copperhead nests in the backyard in the woods, which is a danger to the children of course when the babies hatch out and hide in the lawn. So if the kitties can take care of copperheads--can they? Without danger to themselves? Or will the copperheads be as dangerous for them as they are for the children? Ugh! So many things to worry about...
Anyway--if I do get cats, I think I'll see if I can't get a couple kittens from a farm cat. I do usually prefer to rescue critters--my indoor kitty (no longer with us, alas) was 10 when I adopted him, and my dog is a pound mutt--but I have several reasons for, this one time, wanting babies instead of adult rescues. Anyway, it sounds like what I should look for is a couple of females who are high energy. I figure if I get two, my chances of having at least one good mouser are increased, plus if they're from the same litter they'll be good friends and keep each other company, which I think is important.
By the way, this:
"the animal rightsers who run many shelters look down on country/rural folk who want an animal for practical reasons"
is something I really agree with. I have worked with many rescue groups, and I'm very much in favor of treating animals humanely. But I think sometimes folks take it a bit too far. While I honor and admire people who can give the best of everything to their pets and who treat them like family, I am a little bit old school in believing that it's okay just to provide a warm place to sleep, appropriate nutrition, and basic health care. And that it's also okay to expect a practical return from an animal, and to manage one's livestock in a practical manner, provided that you are also humane.
I am strongly encouraged, however, by the recent movement to try and place formerly "unadoptable" feral cats in barnyard situations. I think that is a move in the right direction.
Anyway. Down off my soapbox. Thank you all SO much for all the very helpful feedback.