Should I use motor driver or Motor driver shield?
The right driver module or shield depends on the motor. Do you know the voltage and the stall current of the motors ?

The L293D uses bipolar transistors for the output stage inside the chip and can only drive 600mA. It has a large voltage drop: the motor gets less voltage than the power voltage applied to the driver. Therefor it can be used with small 12V motors, but it does not work very well with 6V.
The L298N also uses bipolar transistors and also has a large voltage drop.
A mosfet driver like the DRV8833 works better with 6V, because it has a low voltage drop.

In small RC toys with four AA batteries, sometimes a H-bridge is made is transistors instead of using a special driver chip.

The very cheap motor shield with two L293D chips (originally designed by Adafruit) can drive four motors, but it uses many pins.

Bottom line: Everything depends on your motors. I suggest to use a mosfet driver.