That list of parts should be enough to get you started. The Arduino UNO is the most general and widely supported version:http://www.adafruit.com/products/50
For the "finding out how everything works" and "testing ideas to see if this version of the code does what I want" stages, I'd suggest getting a breadboard and some jumper wires too:http://www.adafruit.com/products/239
- full-size breadboardhttp://www.adafruit.com/products/64
- half-size breadboardhttp://www.adafruit.com/products/153
- jumper wire bundle
You'll also need some bits and bobs like resistors to limit the current for the LCD's backlight, plus a power supply and a USB cable to connect the Arduino to your computer. Our Arduino Budget Pack includes most of the above:http://www.adafruit.com/products/193
plus a few LEDs and a few other pieces of common circuit furniture to make experimenting more fun. Our Arduino Starter Pack is pretty much like the Budget Pack, but also contains a Protoshield kit so you can build your final circuit as a shield that plugs directly into the Arduino:http://www.adafruit.com/products/68
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