If it's going to look like an arcade cabinet, then I say make it look like a real one and put a real coin door on that puppy.
Whatever the LED you use, it should have specs on its max current. You can get a handy app for your phone to calculate the resistor to use with your voltage which will give you the amps. Of course, a lot of the LED buttons have built in resistors. In that case, just test it with a multimeter to see what one will draw. In no event would I power them with a laptop USB. They're not really made to do that and will likely create extra heat in your casing and possibly burn out the port. ATX PSUs are cheap or free, or get a wall wort at the thrift store for a buck.