You could use Newton's laws of motion and the inverse square law of gravitiation. Or you could set up some equations using conservation of energy and angular momentum. You will also need the initial conditions, e.g. the speed of the planet at periohelion that gives you the correct aphelion distance.
It's hard to say what is the "best" way to set this up without knowing the bigger picture of how this course fits into your studies. A computer scientist who knows about numerical methods but not much physics, a mech engineer who knows about dynamics but not much astronomy, and an astronomer, would probably do it three different ways.