I saw pictures of your new Appy on your other thread. He should be a very nice trail/daily use horse, after he has some weight on him.
Since this horse has some history of being used by children and maybe riders who were not capable of getting the obedience that they wanted from him, he may have some bad habits. Not a bad horse, just bad habits.
First of all, moving a horse is traumatic, so wait a bit before riding him outside of your arena. Let him settle a bit. Do only ground work and hanging out with him for a couple of weeks. Work on having him be respectful of you on the groundd. One thing, do not take him out to hand graze on a leadline. When he is on the leadline, do not allow him to graze. If he gets his head down, throw the tail end of the leadline at him (if clucking and lightly pulling on the rope doesn't get his head up.) Startle him and if he jumps away from you, ignore that. You just want to intereupt his desire to eat. Over and over until he stands on the lead line, even if grass is under foot.
Be sure to let him graze, but just not when he is on line. And be consistent. NEVER let him graze when online. Make a clear seperation.
If you can, work with him in an area without the temptation of grass while you are getting to know each other. Work on just go/stop/turn/trot/ bend right, bend left. All those little things and make your sessions short and end on a pleasant note.
If you have a round pen, I would do some work in there and even ride him in there. Half an hour will be enough. He may not have the back muscles to support the saddle very well, and this might be part of his crowhopping.
After the two weeks, if you do decide to tackle the issue, let someone who can go through crowhopping and stay on do it first. When they get him to walk away from the grass, then go only a short distance/time and then quit.
Make each thing short and easy to build up the knowledge in the horse that he can trust you not to ask a lot from him. Horse's like to know that there is an end to the work and it isn't just forever far away. Some horses don't care, but others, at least at first, need to have that relief and reward given after a short stretch of the abilities.
Appy's are generally smart horses and often complex and maybe willful. Some folks wont' ride them 'cause of that. But they are also strong, sturdy and multitalented.