DO-WHILE loop --- Waiting for pressing of either of 2 buttons

With a 1 second delay in that do/while the response to the button presses is not going to be very snappy. You would be better off using millis() for timing which would allow you to test for button presses much more frequently.

Have a look at Using millis() for timing. A beginners guide, Several things at the same time and look at the BlinkWithoutDelay example in the IDE