Amman to Petra & Wadi Rum

You can book a tour to Wadi Rum from everywhere in Jordan (but look out that you're going to the protected reserve and not to the "unofficial" one), and most day-tours includes a jeep tour around the main sights in the desert, with a nice sunset view. Food/drink is included, and after your night under the stars you wll be brought back to the entrance of the reserve. If you can make a bunch of people the rate for the tour will be dropped. Have a look at this informative page of a very well-travelled Jordan-expert: http://www.jordanjubilee.com.
For Petra, yes just buy your entrance ticket (for 1,2 or3 days) and walk, walk and walk. I would advice you to start really early, get up to a viewpoint where you can escape the crowds.

#1 assumes you want to sleep with the bedouin, which generally costs more. There are beds available in tents at Rum village which may work out cheaper. In 2007 it cost me 13 JOD (about 12 EUR) for tent bed, breakfast and dinner in the village. On the other hand a full-day (8 hour) 4WD excursion cost 65 JOD per vehicle - I was a "group" of one person so this was a bit expensive, but it did make for personal service and we saw everything I expected.

Thanks everyone,
Some great advice, I feel better prepared now!
Cheers!
Gary.

Gary,
I would spend more time in Petra than in Wadi Rum. Wadi Rum is great to start out in the late afternoon and do your camp, then return to amman the next morning. Petra is fantastic. I would recommend a guide to do Petra to take you to the non-touristy trap choas areas and he could also do your jeep tour, camp and transport from Amman. The site is Jordanartisttours.com. Great, great people.