I think I'll be using the IRF510 from radio shack
No do not, you want a logic level FET, this will not turn on with 5V on the gate.
as well as a resistor (100-200 ohms) from gate to ground, is recommended for mosfets
No a 10K is recommended to ensure that the FET is off when the arduino is off. You need a 100R resistor in line with the gate to protect the arduino's output pin from too much current.
And what is the protection diode for?
To short out a reverse voltage that is generated when turning off an inductive load.