Hi Pale rider
Another dog that shows up at rescue a fair bit is the tenterfield terrier which I think is a variation on fox terrier, similar in look to the Manchester terrier. You'd really want to take the neighbour's dogs to meet any terrier, but especially these, as not all of them are friendly with other dogs.
Whether you get an older dog or a puppy, you will need to go through house training as from scratch - because your place is new to them.
Before You Get Your Puppy | Dog Star Daily
And whatever you do, do not get a dog via the internet classifieds or pet shops. That would be kin to supporting puppy mills which are like battery farms for dogs. And we don't like to encourage back yard breeders either - tho each one of those would need to be assessed on their own merits, accidents do happen to some people who have to learn the hard way how to prevent them. Dogs are pretty amazing jail breakers for a bitch on heat.
You don't have to get a dog or puppy from rescue - tho' we'd cheer you if you did. These are some guidelines about picking a puppy source.
How do I find a good dog breeder? - RSPCA Australia knowledgebase
and when picking a rescue...(pick the friendly dog)
Gary Wilkes Click and Treat: How to Get a Dog