[Updated 5/1]Building a simple calculator.

I would also get an LCD like this one: Serial Enabled 16x2 LCD - Yellow on Blue 5V - LCD-09396 - SparkFun Electronics
What you are looking for is a serial interface for the LCD. This will simplify your life greatly when dealing with programming the LCD, rather than digging up libraries for it, since you just output to a serial port (Which is already setup in the arduino).

Otherwise, I'd recommend digging around and finding the parts you think you need and can afford, and then if you have questions, link the part here and we will probably be able to answer you if it is specific enough.