I travelled there independently, but once at Petra I did pay for a tour guide for the first day. It was an inexpensive way to get a good orientation. We spent three days visiting the site (be sure to hike up (and up) to the monastery.

As for arrival airports, I would vote for Amman. When I arrived (fall of 2000) I flew in Tel Aviv (I wanted to see Jerusalem) and it took quite a while to cross into Jordan. Note that if you arrive in Tel Aviv make sure you have a Jordanian Visa ahead of time, as you need to already have a visa if you want to cross at the Allenby Bridge.

The other advantage to arriving in Amman in it's an easy journey to the ruins of Jerash, which are really worth a visit if you're visiting Jordan:

http://en.wikipedia.org/wiki/Jerash