As the others have mentioned, Overlord Tour is a very popular option with many on the forum, and they seem to be very well rated. Their tours are reasonably priced and use a Van so the groups are on the smaller size. Dale Booth is also exceptional but unless you're travelling with a large group (ie: everyone splits the cost), you may find that Dale's tours are above your budget.
As you have a car, you could also consider Visit D-Day tours (Chris Emery), as he will travel with you in the car and provide more of a personalized tour. You'll have to contact him for prices and other details.
Whichever tour you decide on, it would be a really good idea to book that well in advance.
Depending on your level of interest, time frame and budget, you may want to cover not only the American sites but also British and Canadian, to get a broader view of the landings and the various battles that took place. Some examples of other sites are the Pegasus Bridge Museum or the Juno Beach Centre. Again depending on time and budget, you may also want to have a look at the Maisy Battery, which was only discovered a few years ago (2006?).
One other minor detail. As you may be aware, it would be prudent for each driver listed on the rental form to have an International Driver's Permit, which is used in conjunction with your home D.L. You can easily obtain an IDP at any AAA / CAA office for a small fee.