If you plan driving to Akama/Aphrodite trail have in mind that you should hire a 4X4 jeep and not a saloon car because you cannot make it otherwise. There are plenty of companies to choose from and make sure that there is insurance within the quoted price.
If you plan to explore the island the best way to do it is to hire a car. Travel independent if possible. I advise that you get a good map and try to use the main roads mostly. Petrol is quite cheap but before you set off make sure you have plenty especially if you plan to drive to more remote parts. The advantage of having a hired car is that you can drive to the smaller villages, and stay for as long as you wish.
If you want to get out of Polis and see the island- do book a car before you go. We tried to get one whilst there and could not. This meant it was really difficult to get around outside of Polis itself.
The guys at EKO petrol station must be the happiest workers I've ever come across given that they are working in boiling hot weather surrounded by exhaust fumes. I always make a point of filling up there just in case they are having a bad day and I catch them being less jolly than usual!