If the display is transmissive you need the B/L on.
If transflective one or the other or both, ambient light, B/L.
If reflective you need ambient light.
If B/L is LED best way to control brightness is a PWM driving a pin switching power
to the LED chain.
If pin is the contrast pin, a simple pot to Vdd, wiper to pin, other side grounded.
Regards, Dana.