Tourism Places to Visit in Jordan and how?

Hi,

So I'll be visiting Jordan (Amman) next week on the 29th of March. I'll be there for 3 weeks. I wanted to know what's the best places to visit, and the best way to get there. I don't mind spending a bit extra for safety and comfort in travelling. With that said, brief camel rides would be highly enjoyable as well

Here are the places I had in mind:
- Amman
- Petra
- Jerash
- Madaba
- Bethany Beyond the Jordan
- Mt. Nebo
- Dead Sea
- Wadi Rum

Can anybody comment on if each of the places can be done in a day, something like going from Amman in the morning, visiting one place and coming back by night. I think I'd really like that a lot more.

- What about Petra? Would staying 1 night there be beneficial?
- Also Dead Sea...go to a resort or public beach? If so, how far are they from Amman? and cost?

And last, can anyone recommend any good tour operators that can make some decent packages for far away places like Petra/Wadi Rum as well as local daily tours for the other places mentioned in the list? I heard that apart from Petra/Wadi Rum, all the other places are 1 hour away from Amman can be done on a daily basis (except for Fridays I guess?)

Thanks!