I was dealing with my Arduino / LCD Display project for a wile and being consulting several related topics without luck yet.
The problem that i'm having is that i wasn't able to make the display initialize properly in terms of backlights and character places (dotted boxes 16x2) that should appear on the display once the energy sources are properly connected.
i'm not talking about a contrast problem, since i wasn't able to reach that point of the project yet, it seems to be something related to current or voltage, but i wasnt able to identify the problem.
Follow world conventions.
e.g. Red wires for +5V. Red bus line on breadboard for +5V
e.g. Black wires for 0V (GND). Blue bus line on breadboard for 0V (GND)
Of course you might run out of the correct coloured wires.
Choose Red, Orange, ... for +ve. Black, Blue, ... for -ve.
Or use plain solid core wire that you cut to length. And lay the wires neatly on the breadboard. So you can see exactly which holes they plug into.
This will take 10 minutes from your life. But it will improve your hair retention.
OK , you need to connect the contrast voltage - pin 3 - before you expect to see anything on the display. Connect the wiper of a potentiometer - 10k or even better, a 1k - to pin 3 and one end to ground. Do not connect the potentiometer to Vcc. Adjust it until you see a row of blocks on the first row (only), then proceed and connect the other pins.
... be aware that the breaks (near the number 30) in the blue and red lines on your breadboard correspond to breaks in the corresponding horizontal bus bars.