Which mosfet to use with 4 TEC1-12709 peltiers (Arduino MEGA 2560 board)

In series or in parallel? Using PWM? If so what frequency? Higher speeds of PWM would
really need a MOSFET driver chip to get fast switching.

If you want to drive the MOSFET directly from an Arduino you must get a logic-level FET.

What maximum current are you needing and what's the power supply(see my first question)? You need to calculate
the power dissipation in the FET using I-squared-R (ignore the nominal current rating of a MOSFET,
its only applicable if using extreme cooling measures).