Help planning a week long trip to Jordan?

So, I M25 from the UK, I have booked to go to Jordan for a week in mid November, going from Saturday 12 November to Saturday 19 November.

I fly into Aqaba direct from Gatwick on the 12 November, and I planned on spending two days there just to acclimitise. I understand that there is not much there, and it’s more of a resort/beach town than anything else so fancied a couple of days there to relax.

I then planned on going to Wadi Rum and staying there for a night to check it out. I understand that there are hostels there, however, how easy is it to get from Aqaba to Wadi Rum?

Similarly, I then plan on going from Wadi Rum to Petra. Is there a direct bus from Wadi Rum to Petra? Or would I have to go back to Aqaba and then go to Petra?

Similarly, that would take me up to Tuesday to arrive at Petra. How long should I stay in Petra for 1 or 2 nights? Once I eventually get to Amman, was it worth booking a tour of the dead sea? Or can I DIY it?

Thanks in advance!