Firstly, I'm glad to hear you adopted an American Staffordshire Terrier cross!
This is a breed that matures pretty late, so this behaviour is quite common. The best advice I can offer you (I own 2 pittys, and rescue tons more) is to teach your dog to wait (it's the same as a stay, however can be released no matter where you are with an "Okay") And teach your guests not to pet or give any attention to your dog until she completes a sit. That should be the only time they can pet her. She should be rewarded for this. What I do is keep a pretty container near my front door with treats in it for my guests and clients to give my dogs and my foster dogs. People really like to see that they can make a dog do a trick, even if it's as simple as a sit so both sides will enjoy this.
To control the barking, I teach my dogs to bark on command, and to stop barking on command. When she barks say good and give her a treat. To get her to stop say "Shush" and wait till shes quite and give her a VERY happy good and treat her. This is a smart breed, and she should catch on very fast.
It's really nice for guests to walk in, and have a dog sitting and waiting for their attention. And it's easier for you, so you don't have to apologize as much as before for her jumping
If you have anymore questions feel free to email me at firstname.lastname@example.org
I deal commonly with the pitty breeds and mixes.