I cannot recommend a dog for you (other than a toy breed) unless you have a fenced yard.
Without a fenced yard, you would need to take your dog outside on a leash even for bathroom breaks. This really isn't fair to any dog larger than a Maltese or Chihuahua. Dogs need a fenced area in which to stretch their legs and run around a little, on the grass, several times a day. Dogs don't like being tethered to a leash all the time.
It isn't safe to just let a dog outside "to do his business" in an unfenced area. Dogs have the mentality of a 2- to 4-year-old child and they can outrun an Olympic sprinter. If anything catches their attention, they will take off and you'll never catch them. Putting one's faith in "boundary training" has cost countless dogs their lives.
Your fence must be a physical fence. In my opinion, invisible fencing is neither safe nor secure.