This is a pretty simple task for something like an Arduino.
I would buy:
Arduino http://www.sparkfun.com/products/10356
Serial LCD display http://www.sparkfun.com/products/9066
Pushbuttons http://www.sparkfun.com/products/9336
Buzzer http://www.sparkfun.com/products/7950
The only thing that worries me is your shock sensor input at 3V. In an ideal world, the signal would be enough to trip a 5V logic Arduino input, but in the real world it might have issues including noise. But nothing that some extra circuitry would not solve.