Peter,
PM sent separately, but plan to go scuba diving in Aqaba. Next to Ras Muhamad off the Sinai, it's one of the best scuba locations in the world.
Wadi Rum is great for camping, but plan to freeze at night, even in March! But for trekking, it's amazing. Also, if you stay at the Dead Sea for a couple of days, there are some really great treks to do in that area as there is a spectacular gorge that can only be hiked nearby.
Plan to do a day trip to Jerash, too, as it is a beautiful Roman city with great ruins (yes, even if you've been to Italy, it's still worth seeing!).
When you say "hire a car," you might want to consider hiring an English-speaking driver along with it. English is not spoken that much outside the hotels and tourist areas. The cost is reasonable.
As for hotels, PM me. 4 and 5 star hotels will run in the range of 100 - 200 Euros/night and while cheaper ones are out there, the difference can be pretty big for the money saved. All depends on the budget, of course.
Plan on a minimum of two days in Petra. You can hike to your heart's content in Petra and they sell multi-day passes for just a little extra money. One day is around 20 Euros/person and three days is maybe 30, so it's a good deal to stay on. There is so much to see and photograph there that you will want to take the extra time.
Keep in mind that March is ultra peak time for Petra so crowds will be huge. If you get a hotel at the entrance (Movenpick or Petra Palace) you can be at the gate when it opens and get in there to photograph in the soft morning light before the mobs hit. The best shot I made of the Treasury was at 0800 or so and I was all alone there when I made it. Try to get to the Treasury and the Monastery early . . . .
Wadi Musa is a landscape photographer's paradise! You'll need to hire a Bedouin driver with a 4WD to do it, but be sure to hire your own and not get put into a group. Cost a bit more, but you'll have time to stop and photograph and not be rushed all the time. Plan on a full day in Wadi Rum. Also, the Dead Sea has some spectacular salt and stone formations around it (along with hiking in the nearby gorge and, of course, swimming and spa treatments!), so you might want to base yourself there for a couple or three days. Incidentally, Movenpick has a wonderful "village" resort where each room is like a traditional Arab house -- quite charming, but not cheap. My own preference is the Dead Sea Marriott and the price is reasonable.
Don't expect to buy any film in Jordan so take plenty with you. Incidentally, security is quite good (read "high") in Jordan so lead bags for the film are good, carry your cameras with you, be careful where you aim your cameras (NEVER photograph a soldier or policeman without asking first!!), etc.
The Jordanian people are about as friendly as they come. I'm obviously American, had a Palestinian driver, and never got so much as a dirty look from any of the 100s of people I encountered and dealt with during the two weeks or so I was there (over Christmas and New Year's). They are simply wonderful, engaging, delightful people and you need not worry or expect any trouble from anyone. English is widely spoken at a simple level in shops in the cities, but expect to encounter many people who do not. In Aqaba, Petra, and Amman, you will not have any real problems with English, but elsewhere people may be monolingual. A few key phrases in Arabic will go a long way to generating good will for you.
I've been to Jordan many times and never fail to be impressed with the country and the people. It's a wonderful place and your trip there will be quite memorable. Have fun and stay safe!
