What is the most suitable? Pull Up or Pull Down
The ATmega328p I/O block only provides pull-up functionality. There is no internal pull-down. I've circled the relevant bit of the circuit in the diagram below -- notice that there is no "mirror" of this circuit to pull the pin to ground.

(It is, of course, still possible to drive the pin to a hard low. However, this is not suitable for use as a pull-down; the pin will always read as low if it is being driven low, and the I/O block may be damaged if it is forced to sink more than its limit of 40 mA from a pushbutton.)

If you disable the internal pull-up resistor, you can certainly hook up an external pull-down resistor. There is no significant advantage to doing so, though, especially for a low-speed I/O like a pushbutton.