All you really need to start you exploration is an Arduino. However, to complete this project, some other optional items are needed:
Jumper Wires like adafruit.com/products/758 for (Step 2)
Breadboard like adafruit.com/products/64 (for Step 2)
7-segment display like adafruit.com/products/881 (for Step 2)
Piezo speaker like adafruit.com/product/160 (for Step 3)
Tactile push button like adafruit.com/product/1119 (for Step 4)
RTC module like adafruit.com/products/264 (for Step 5)
4xAA Battery holder like adafruit.com/products/830 (for Step 6)
5mm or 10mm LED
Project Case