I’ve adopted two “mature” dogs, both of which ended up being incredible additions to our menagerie. (three dogs, five cats and four fish) One dog required a little extra training (wasn’t used to being on linoleum or running since she’s been chained for most of her life) but was very good-hearted and great with the kids. The other dog was a sibling of a dog I already owned and despite having been with two other owners over a space of four years, he fits in well since he shares most of the same habits his sister has…the one exception being he’s very hard on stuffed toys and she’s had most of hers since she was a young puppy. I swear she had tears in her eyes the first time he grabbed one and started ripping the stuffing out of it!
Get as much history as you can about the previous life the older dog has-it helps to know about any potential problems in advance like being scared of cars or being a cat-chaser,etc.