Which OR Gate to use
I would say: none of the above.

Let's take them one at a time.

The first one you are assuming enough current from your logic outputs to drive the LED. You also need to take into account the voltage drop from the diodes.  With silicon diodes that can be as high as 0.7V.  It would work, and you don't need the 10KΩ resistor as it serves no purpose at all.

The second one the transistors are in the wrong place.  They should be below the LED, not above it.  The voltage to switch on is relative to the emitter, and with the LED and resistor in that path you're offsetting that voltage a lot.  You should have the emitter to ground and the LED on the collectors.  See my circuit below.

The third one I actually have no problem with, and if you want to use a chip then that's fine.  Be sure to choose one that can source enough current to drive the LED.

The discrete component option I would use would be to use a pair of NPN transistors:







simulate this circuit &ndash; Schematic created using CircuitLab

With that arrangement the inputs aren't inverted (either HIGH turns a transistor on), and Vcc can be any voltage you like (with the right resistor and suitable transistors of course). The LED can draw as much current it needs to and isn't limited to just what the logic outputs can provide.



By the way, the layout of your circuits is not easy to follow.  Especially the habit you seem to have of letting your ground points stick out at all angles.  A good schematic has:  


Inputs to left
Outputs to right
+ve voltages to the top
Ground to the bottom
(If you have them) -ve voltages right down the very bottom.