Although I believe the 10-inch cast iron skillet is the most essential pan, I think a good 8inch non-stick skillet works great for eggs, pancakes, and grilled cheese. When you are looking for a non-stick skillet look for a ceramic coated and dishwasher version.
Remember to use plastic kitchen utensils to avoid the finish from scratching!
I recommend: Blue Diamond Infused Ceramic 8-inch Non-Stick Skillet.