A lot depends on

Age of the Travelers

How much luggage

Your transportation budget

How good you are at negotiating through a busy international city without knowing the language

I found this website quite helpful in planning for Turkey:

http://www.turkeytravelplanner.com/go/Istanbul/Transport/gokcen2ataturk.html

The cheapest is to take the public bus with a change of buses at Taksim Square. This is not quite as easy as it sounds. If memory serves, you go to a bus stop and there is some kind of monitor and you just tell him "Taksim Square" and he'll guide you to the next bus going there. Lots of people will be waiting and plenty of buses will be arriving and departing. I believe, however, that the airport bus stops are less crowded.

There is also a shuttle/limo service which you can arrange in advance. This might be the safest and most convenient.

You can also hop a taxi and let the taxi driver worry about the traffic. This is probably the most expensive mode.

I also found a more exotic way to go by sea, but that involved taking a bus to one seaport (forgot its name), catching the ferry, then taking a bus to Ataturk at the other end. One day, with no worries about time, I'll do this.

Hope this helps a bit. Have a great trip! Sounds like fun!

We are 22 and 32, both female.
We have 1 luggage each, less than 15 kg.
I am fluent in Turkish but I am not familiar with Istanbul, that is why I was asking

Thank you!