I guess thr right dog will just feel right won't it?
I would spend as much time with a new dog as possible, especially as you have kids and don't get your heart set on any until you know they are suitable for your family. For your situation I wouldn't recommend a dog that seems timid, anxious, sensitive or really intense (e.g. if they are really protective of a ball). Make sure you check the dog out to see if they are sensitive around different parts of the body (e.g. that they won't bite if their tail gets picked up by a kid, or hate their paws being touched). Ideally I would choose a dog that shows relaxed, calm behaviour in lots of different situations (other dogs, cats, walking on a lead, playing with kids, around food etc.) as I believe that lowers your risk of issues like biting. Another thing to point out which you probably know is that it is really hard to get rentals with dogs now. There are other non-permanent ways of having pets in your life like fostering a pet if you think you may have to move a lot in the future. Good luck! xoxo