We used Jordan Direct tours. I had found favorable comments about their services on TripAdvisor. I have no personal relationship with this company. Their website:
http://www.jdtours.com/
On the home page, you will see that they offer "Tailormade Jordan Tours." Also on the home page, look for a link (on the lower right side) to the 8 day "Jordan Classic Tour."
Basically, we started with the Jordan Classic Tour itinerary. I purchased and read (and brought along) a Jordan tour book, and I found a few things (primarily Christian sites in Jordan, such as the St. John Baptismal site) that would interest us. So I worked with the tour company to make some modifications in their Jordan Classic Tour that we felt would suit us better. We used some of their hotels, but I also had my hotel reward accounts available. So they allowed me to make my own hotel reservations (using points) in several places rather than use their hotel. Using my hotel reward accounts reduced the overall price of the tour.
Jordan Direct provided the driver and car. The driver was just that - a driver. He was not a tour guide. So at some of the locations we visited, there was a short private tour with a guide arranged. At others, we were on our own (but I had my Jordan tour book to follow). For example, in Petra, they provided a guide for several hours and then we spent the rest of the day exploring on our own. I remember that the driver was a young man named Ibrahim. He had lived in the USA for a number of years and spoke flawless English. He was enthusiastic about showing off his home country to foreigners and we enjoyed him very much. This was back around 2010 or 2011 as I recall, so I have no idea if he still works for them or not.
One funny story: our original itinerary (similar to their Jordan Classic itinerary) proceeded from northern to southern Jordan. We were then to return to Amman for an overnight and fly on Royal Jordanian to Tel Aviv to begin the Israel portion of our trip. This is one of the ways of crossing from Jordan into Israel. Well, RJ cancelled our flight a few months before our trip, leaving us high and dry with no good alternative flight on the same day. I already had everything set up in Israel and did not want to change all of our reservations in Israel to a later date. (And I definitely did not want to screw up our 2 award seats in J returning to the US from Tel Aviv on El Al.) So we worked with Jordan Direct and asked if they could drop us off at the border crossing from Aqaba to Eilat. Our Jordanian driver could not take us across, but we could walk across. And that is exactly what we did. Walking across the border from Jordan to Israel was like being in a classic spy movie where the Western spy is being released from a prison behind the iron curtain. First you go through Jordan customs (and make sure to have enough Jordanian money to pay the exit fee). Then I rolled our luggage across no man's land between the two countries. The Israeli border guards had nothing else to do, so our luggage was thoroughly searched. Fortunately, a taxi was waiting on the Israeli side. We took a hotel for one night in Eilat and then flew the next day from Eilat to Tel Aviv to being our Israel itinerary.
Going through Israeli airport security is an interesting experience. I have another story, but that will be for another thread.