My previous dog was 1.5 yrs old when I got her, and to this day I know very little about her background except that she was a WGWL that was raised in a household with 7 children and many other animals. When I got her she had had a litter of puppies, and the people wanted to get rid of her too because they couldn't afford to get her spayed and they didn't want any more puppies. I went to get a puppy, but they'd just given the last one away earlier that day. So I ended up with mom! When she came home with me she would growl and show her teeth when approached by any child shorter than 4 ft tall, and acted sort of fearful when approached by new people. Essentially she was a mess LOL! What she became still amazes me, though, as a more intelligent, stable, obedient, and loyal dog would be hard to find! By 3 yrs old the dog would hold a stay in a new, unfamiliar location for days if asked (actually did that on a couple of occasions), and she was stable enough to take anywhere with me offleash. In fact, though I was stopped a time or two by animal control for having her offleash, I'd just show them the control I had with hand signals and was never ticketed! She was an amazing dog!
Though I know other people who've not had great experiences with a rescued dog, a lot of what you end up with is on you. All dogs need stable leadership, puppies included, and training. The really great thing about an older puppy or an adult dog is that you often have a better idea of what they're personality is like when you adopt them. Puppies can be a crap shoot, and they need much more attention early on. I'm not trying to talk you out of a puppy, but they can't go all day without pottying and exercise, so if you can't do that personally you'll need a neighbor, friend, or family member to help you out, or you'll have to hire someone if the other options aren't available to you. To put things in perspective, read through some of the issues people have with puppies on this forum, either in the puppy section, or in the aggression section. And best of luck to you whatever you decide!
It's not the size of the dog in the fight, it's the size of the fight in the dog. Mark Twain