Besides your basic kitchen utensils and appliances, there are three must-haves I have found to be extremely helpful:
1) Slow Cooker (most commonly known as a Crockpot, but they ain't paying me to advertise for them)
2) George Foreman Grill (they ain't paying me either, but if I said "indoor electric grill," you would have no idea what I was talking about)
Foreman grills can be a wee pricy, so you might wanna hit up Mom and Dad for this as a gift. Just tell them you are trying to cook healthy!
Foremans are great cause you can cook up some meat SUPER fast. Like a steak takes about three minutes. If you miss the flavor of outdoor grilling, you can always add a couple drops of Liquid Smoke to the meat (found near the BBQ sauces at the grocery store.)
The only thing that sucks is cleanup. A lot of the newer ones have removable plates you can wash, but if not, run a paper towel over it while it's still hot for easy removal! Otherwise you get a stanky crust, and no one wants a stanky crust.
Kinda random, I know. But I am a big fan of these. It makes it WAY easer to pour olive oil so you dont end up dumping out a whole bunch at once when you are cooking. It also makes it easier to drizzle oil on top of food.
Less oil dumping out = saved calories and saved money. Also, you look like a bad ass chef using it.