my vote is for independent travel
Petra is perfectly easy to organize independently. as previously mentioned, easiest is to fly into Amman, then rent a car at the airport and drive straight down a perfectly straight and well-maintained highway to Petra. there, you can hire a local guide if necessary. however, I found that a good guidebook is all you need. compare the costs - if organized tour is much cheaper, then maybe its worth it. also, many interesting stop on the way down (crusader castles, biblical places, etc). great way to make a day of it getting down there. Hertz and maybe others allows you to pickup car in amman and drop off in petra without any additional fees on rentals of 3 days or more. although you'd probably need to come back to amman to fly back as well.
another thing to note - i saw the tour groups in petra and I spend MUCH more time there than the groups were allowed to spend. also, some of the magic is being in quieter places without another 30 people with you, some of the quieter corners. impossible with a tour group. Petra is huge and there's a big choice of places to go or not to go. i would not want to have to follow the majority rule and go to some places and skip others.
if you can fly into Aqaba, it's about 1.5 hr drive, also on good highway. Jordanians are very friendly, polite and many speak english. I was traveling alone and had no problems whatsoever.