A 3-pin fan is most probably one that has a tachometer output. It has no speed control. A 4-pin fan would be better because it can be controlled directly from the Arduino pin.
You can only control the speed of a 3-pin brushless fan by controlling the power supply voltage. You can do this by making a PWM-based power supply but that's going to be relatively large, bulky, inefficient and expensive.
Buy fans that are intended for this speed control.