Keep it simple. :) Start out with the walk and trot. Work on your position (ear to hip to heel) and keeping your hands quiet, even when your body is moving. Practice a consistent, even walk and trot on a loose rein. Practice making your horse (walk or trot) faster or slower with only your seat. Practice transitions up to trot, down to walk, stops and backs. Practice making world's most perfect circles.
On the ground (when you're leading her in a halter), work on getting Penelope to show you her manners! Practice making her stop with you, back with you, and turn without invading your space. Practice picking up her feet, petting all around her body, and if you're giving her treats-- play a game where she has to look away before she gets the treat (trust me, they pick up on this one quick.
All of these simple things seem simple in concept, but they take some time to "figure out" when you're a new rider on a new horse! Good luck!