You'll probably want to base out of tlapacoyan - staying at aventurec is the way to go. The reynosos are great people and it's super convenient. They have great selection for boat rentals and have drivers who are familiar with all of the local runs who will run your shuttle. housing options range from camping to hostel to cabana, and the food is great. Recommend doing the breakfast buffet which will tie you over until dinner which is easy to do in town. A car isn't really necessary- you can hop on a bus from mexico city pretty easily. Unless you've got a fairly large crew and want a lot of flexibility i'd say it's not worth it. You'll end up spending a lot more than the sticker price on insurance and repairs. Not to mention you'll still have the issue of shuttles and 4x4 roads.
It can all be done pretty cheaply, flights will definitely be your biggest expense