Graphing calculator project

Projects General Guidance
1

Hey, I'm trying to build a graphing calculator that is a clone of popular TI or Sharp calculators. I want an LCD that can display graphs, a keypad, and about 20 extra function buttons.

  1. Which board should I use?

  2. How do I wire up ~20 buttons to the Arduino?

  3. Rough guidelines of how to program the graphing bit of it? How do I create and display a graph?

  4. What other parts will I need, aside from these:
    Resistors (what rating?)
    Breadboard
    Arduino board
    Buttons
    Keypad
    Cables
    LCD
    Casing

Thanks! (this will be my first Arduino project ever, so sorry for noobishness)