I live in the Chicago suburbs and there is a decent sized coyote population near my house. More than one "yapper" has been snatched. Hawks have also gotten a few.
My last dog, in the early 1990's, was a purebred Dalmation that I ended up having to put to sleep when she developed some emotional issues at the death of my stepson. Brother-in-law has a beautiful purebred collie that has cost him in excess of $15,000 to tend to her medical issues.
Definitely want a rescue "mutt" for just about all of the reasons that you have listed.
Up here it's coyotes and hawks, but also stray dogs and owls. Gigantic owls.
If you were in my neighborhood, I'd say you could snag one of the mutts off the local reservations. They usually have about a dozen strays running around at any given time.
But a neighbor I know who did that paid the vet over $1000 just for meds and shots for a stray he picked up, as they have a lot of health problems. Plus they're very tough to train, having been wild for some time. My neighbor's dog still had major behavioral issues and eventually had to go be destroyed after it attacked a few people. Normally the SPCA just euthanizes these strays, and considering the shape of those dogs maybe that's a good idea all round. I wish they'd fine the "owners" that let them stray in the first place too.
But that's an extreme case. You will likely have better luck than my neighbor.