Disable other buttons while one of buttons is pressed
The best solution for this is a finite state machine. There are lots of tutorials on state machines, just google.

Finite state machines are a very important concept in coding. You will find the need for them everywhere. Do yourself a favour, and read up about them, practice them, understand them, love them. Understand when they will be useful, and when they are not. If you do not, you will be back here shortly, with another question, which could also be solved by a finite state machine.

I strongly recommend you use this task as a practice task for learning about finite state machines.

Note also that, in electrical circuits, you frequently get bounce - when you push a button, your arduino will see many "button presses" (from off, to on, back to off), until it settles down. See http://blog.kennyrasschaert.be/images/20140401/Bouncy_Switch.png for example. A state machine can also help you with this. 

If you don't want to learn about FSMs, read on:

initialise last_button_pressed to 0 (meaning no button pressed)
if last_button_pressed&gt;0
   if not(is_button_pressed(last_button_pressed) then
      last_button_pressed=0
else (no button is pressed)
   for each button_to_check (1,2,3)
      if last_button_pressed=0 and is_button_pressed(button_to_check) then
         last_button_pressed=button_to_check