Clyde, advanced booking of car in Cuba is absolute must, especially for high season. I travelled there in May of 2018 and pre-booked in January. The cost was 93 CUC/USD per day for medium automatic (and very basic) Renault for 12 days. However, if you plan to travel Road 20 (it's oceanwise road) from Desembarco del Granma National Park to Santiago de Cuba please check the state of the road and better plan to take more reliabile car (like Jimny), broken bridge would be not the biggest problem on that road; and in general, if you plan epic trip around the country, you could imagine what the road conditions are. I used this site for the booking http://eng.ancontur.com/avto-cuba.html.
It was recommended by the most popular travel Russian forum (Russians travel a lot to Cuba). Check their rates - they are basically taken from the largest car rental companies and they act as agents. Please note that many car rental companies only operate through agents and will never reply to you.
I prepaid the amount of rental in full at the time of booking - this is also usual practice for Cuba, you will get voucher and go to the rental company with it when in Cuba (I took the car in central Habana). Also, in general, note and study many hints, recommendations, useful advice (like taking Euro, not USD; being very careful when exchanging currency; create a reserve of internet scratch cards), Cuba is not an easy destination, be well prepared. During our stay, we only met with unpleasant situation once (some folks on the road to Vinales were trying to press, saying that I didn't stop before stop road sign, probably in hope to get some money, but didn't succeed).