Maybe the dogs bark at yours because they can tell he's not really stable. (I don't mean like he's unhinged, but as Cesar would say, not a balanced calm-submissive animal.) You seem to really be hung up on feeling sorry for this dog, and that's not the way to move forward. The best thing at this point is to show supreme confidence and quit worrying so much. Then you need to quit focusing on getting him to "like" other dogs because, as was pointed out, this is a Pit Bull. (Or AmBully, but still...) Bred for 100+ years to do combat with other dogs, so you have to expect at least some degree of dog-aggression. Your dog may not be a standard gamebred dog, but he's probably still got a glimmer of that drive.
There is no sense in using a muzzle at this point, as that has the potential of making him more defensive. Go back to the basics. First, before you take him out for socialization, get him tired. Put him on a treadmill or play ball with him for 20 minutes. The excess energy when you're trying to work with him is doing him no favors. Then get him out in public, but don't force him into any dog-on-dog encounters. Don't make a big deal about what's going on around you. Bring a pouch of treats and set yourself up in a park or somewhere that there are distractions around, but not right in his face. Then work on your obedience training while letting him get used to what is going on around him.
If another dog comes up to you, reel your dog in and put yourself between your dog and the other. Be firm and tell the other dog to go away. It sounds like he might be going through a bit of a fear stage, and he needs to know that he isn't always "on guard," and that you have the situation in hand.
And yes, by all means, save up the money and go to a good training class. Any instructor worth their salt will know that the dogs aren't going to be perfect to start off with. But it will do your dog a world of good to be in a controlled environment where he can be exposed to other dogs, but not be expected to actually socialize with them. He needs time to simply be around them and get his confidence up before you take the next step.
Good luck! Keep at it. Be confident. Quit worrying so much.
ETA: As for the jumping up, that takes time to break. Start teaching your dog to sit before greeting, and don't let anyone pet him while he's not sitting. He will eventually start sitting on his own when he sees another person. That's the beauty of associative learning.