I know no one has posted here for awhile, and yeah, I'm a gal. *swoon*
Of course a good cutting board and knife set.
Crock pot, George Foreman, a good dish that will steam in the micro, I got a great one from Pampered Chef.
But the simplest, especially when cooking for one is Zip Loc Steam bags. Toss everything in the bag, microwave, eat!
For a good fry pan, while it's a bit of a learning curve, Cast Iron! Properly cared for, you'll never need to buy another fry pan. And they come in all kinds of shapes and sizes, including dutch ovens and griddles with ridges to drain the fat off of food while cooking. You can use them on the stove, in the oven, on the grill, campfire, if you've got heat, you can cook!
If you haven't done so, join Pinterest. Tons of recipes. YOu can search for anything and find all kinds of tips and tricks. Another great place is Instructibles. They have an awesome phone app. It's also more a manly place.
I do have to say my most beloved kitchen gadget is the crock pot. I've invented recipes, adapted recipes, it's kind of like having someone cooking at home while you're gone. I have one large, on medium, some days have both going, and am going to find a small, ( for 1 to 3 servings) one.
In the summer the outdoor grill. Scored some sweet veggie racks/holders that will hold 4 skewers of food, etc. at Wal mart for doing veggies, shrimp, fruit etc. I do bacon on the top rack, on low, on my grill in the summer.
When cooking bacon, the broiler rack that comes with your stove, is your friend. Do bacon on it, in the over at 350. It does take awhile, and you have to turn it about halfway through, keep an eye on it the first few times you do this, because it can seem like it's taking forever, it does take a bit, but towards the end, it becomes easy to burn it. But the best part is the grease all drains off into the bottom of the broiler pan.
A beer can chicken holder and big a$$ pot. You can season it with anything! Empty pop or beer can, fill it with whatever you're in the mood for. Slap the chicken on, add some water in the bottom of the pot, set burner on low and later, enjoy!
I also have a food dehydrator, for doing my own fruit and jerky. And a pressure canner so I can preserve the wonders from my garden. Along with an ancient, but tough meat grinder, great for processing our deer, making goose/duck sausage and salami, etc.
I think I'll stop with the pressure canner, probably more than you wanted to know.