In her weekly newsletter The Splendid Table Lynne Rossetto Kasper gave suggestions for bridal shower and graduation gifts- things she considers essential. She had suggestions I hadn't thought about such as timers and oven thermometers. And I admit they are essential to success.
Here's my list for someone who is learning to cook and bake.
An oven thermometer, timer and instant read thermometer
A microplane grater, a citrus reamer, a vegetable peeler with a ceramic blade (It doesn't rust in the dishwasher)
Quality measuring cups and spoons (I have a set of magnetic measuring spoons that are so convenient. They are held together with magnets so they're easy to find, but you don't have to wash the whole set and they have flat bottoms so you can measure liquids ahead
Silicone spatulas and quality wire whisks, a pastry blender, a pastry cloth and wooden rolling pin.