My no. 1 recommendation to any young person learning to cook is to master three things:
1. A good fried rice
2. A good stir fry
3. A good omelet
These three things alone will mean that you'll have substantial, delicious food at the ready. They're incredibly flexible in terms of ingredients and need minimal skill. A stir fry or fried rice can take any vegetables or meats you have at hand, and an omelet can take everything from ham to mushrooms.
Strongly second the first two, strongly oppose the third. Omelettes are far too difficult for a beginning cook. Fritattas on the other hand are trivial (you just pour the eggs/milk into the pan after you've cooked the filling a bit).
1. A good fried rice
2. A good stir fry
3. A good omelet
These three things alone will mean that you'll have substantial, delicious food at the ready. They're incredibly flexible in terms of ingredients and need minimal skill. A stir fry or fried rice can take any vegetables or meats you have at hand, and an omelet can take everything from ham to mushrooms.