You can purchase an AKBIL (sold in major stations such as Taksim). You can load credit on it. (It sorts of work like OYSTER of London). You can use this on city-run vehicles such as busses, trams, boats. Enjoy your stay in Istanbul.
Actually AKBIL gives chance to use the second vehicle on a limited time after you used the fist one.
Also you should pay to buy it. If any credit left inside it will turn out garbage.
So either you can buy tokens in all around all tram lines or metro station. In the public buses there are private buses with blue color and green ones belongs to municipality but both of them accept payments in the bus.
The most easy way is private transportation. It is not so expensive as you think. There are online websites like http://istanbulvipairportmeetandgreetservice.com/ where you can check for the prices and book the service. Public transportation is not good for you, especially if you have plenty of luggage. If you take a taxi, the price will be almost the same as the private transfer.