I have a vertical cocktail cabinet.. one side has a joysitck, spinner, and two buttons. The other side has a joystick, trackball, and three buttons.
I haven't run across many vertical games that require the 3rd button.. Asteroids and Space Duel benefit from a 3rd button, but you're not getting accurate play on those games with a joystick anyway.. (and you can always remap up or down to help out on those games) A third button would have been helpful for Star Trek, but that's a spinner game.
I think you'll be fine with 2 buttons. I've been playing my vertical cocktail cabinet for years and haven't regretted the 2 button layout.
Good luck,
88mph