I had arranged a private tour. The guide picked us up from the ferry in Aqaba (we had been diving in Sharm), did the visa/immigration stuff and drove us to Petra. I would have liked to have had another day there. I think at least a day and a half if not two days would be idea.
I agree that it's do-able on your own. The question is whether you like tours or not. I hate tours, but others love them; it's just a matter of taste and disposition. There are other sites I want to see in Jordan (Jerash is the major one). You might also want to arrange a night in Wadi-Rum. We didn't, but I'd love to do that. I think there are some eco-tourism things there.
Almost everyone I met (including the Bedouins selling stuff) spoke at least some English.
The Jordanian government is under heavy financial pressure. They have taken in a lot of Iraqi refuges and tourism is down because of the unrest in the Middle East. If you go, please buy lots more than you need, especially from the Bedouins who are dependent on the tourist trade.