Booked with Wadi Rum travel camp. We had very good experience with them, Better to go in December if planning for Wadi Rum as you will be doing activities, climbing rocks and crossing desert so weather should be cold. If you have young kids (below 12) visit The Children's museum in Amman. In Petra book 2 days ticket. 2nd day go for the Monastery on the top.

 You can visit the authentic and not-so-authentic religious sites. Most probably all burial sites of Sahaba are authentic. The ones of the earlier prophets are not really confirmed.

 Visit site of Yarmouk battle, Kerak castle ,Ajloun castle, it has a cable car to access it too

If u r interested in roman ruins u can visit Jerash. I dont have much interest in them.

 I would recommend a night camping in Wadi Rum, 2 nights better 

Snorkeling and scuba diving in Aqaba is also good.

We visited last year with a group of friends.

A colleague recommended a driver who picked us up from the airport and showed us a lot of Jordan landmarks in 3 days. worked out cheaper than multiple Uber rides.

Day 1:  Started off in Amman, the capital city. ancient ruins right in the heart of the city. enjoyed the traditional rice dish called Mansaf, I will share some of the recommended restaurants pics.

Day 2: Umm Qais and Jerash, had  a day trip to Umm Qais, which offers views over the Golan Heights and the Sea of Galilee. You can see the border of 3 countries from that point , Jordan, Syria, and Israel. The ruins of the ancient cities of Gadara were fascinating. Afterwards, we headed to Jerash, famous for its remarkably well-preserved Roman architecture. On our way back visited grave of Hazrat Abdur Rehman bin Auf RA.

Day 3: Spent whole day in Petra and on our way back drove past Dead Sea, by that time it was quite late at night.

Visited Ashab Kahaf cave (companions of cave) on our way to the airport.

We couldn't make it to Wadi Rum or Ajloun Castle built by Salahuddin Ayubi, which was highly recommended by friends. The people in Jordan were incredibly friendly and welcoming. Plus, we had a great driver who made our journey smooth.

Overall, it was a very good experience filled with history, culture, and natural beauty.

Highly recommend adding Jordan to your travel bucket list.