On topic: we've used invisible fences before, and they work great. Your other, cheaper (but more unsightly) option, would be to build them a sizable dog run/kennel to put them in when you're not there. Good luck with the adoption(s). I've had 3 or so pound dogs & they've all been wonderful. If you can, have a vet check them out before finalizing the adoption, just so there aren't any surprises (expensive ones).
The reasons I will never get a pound dog: Mutts are ugly. I don't want to be scared when my dog is around little kids. If I'm going to put 12 years of time and money into something, I want to know what I'm getting.
Meaning what exactly? Trust me, you'll be getting a dog. As someone who has been around both tons of pound dogs and high priced, breed specific, show dogs....at the end of the day, they are all still dogs. Behavior thereafter is more about the owner then the dog. But if you feel better treating them more like cars or tv's, go to town. Just please don't be one of those people who has their own little puppy mill running trying to sell $500 puppies outside a Randalls or Kroger.
The SPCA tests dogs for their behavior around little children and babies. If the dog doesn't pass the test, they won't adopt it out.
Okay, you IF users... If you just want to walk your dog, how do you leave your property? Does the dog respond to aural stimulation or vibration in the collar or do they learn to rely on visual signs, too? Say you just want to walk your dog up and down the street... what's the technique for getting them to willingly leave the property or do they just go if they don't ge a signal of some kind to stop?