You don't generally need to take anything smart, but a few people in the group dressed up on the evening in Aqaba.
I was expecting to be cold in Wadi Rum but I was actually too warm at night (at the end of November). I did take a decent sleeping bag though, and a small hot water bottle (a kettle was kindly put on the fire for me to fill it). You can sleep in tents on camp beds (two per compartment) or on cushions outside around the camp fire.
Be prepared for a range in quality of accommodation, even within the same hotel. You may have a nice room one night and a not so great room the next, but it will generally even out over the week. The hotel in Aqaba was the best quality of the ones we stayed in.
The Cave Bar by the entrance to Petra is quite smart and does great cocktails. The only hotel to have a bar was the one in Petra, but you could generally buy alcohol nearby the others to take back to drink at the hotel if you wanted to. Food was more expensive than I expected.