Complete cooking sets are kind of a waste of your money - you'll end up with pots or pans you never use that just clutter your kitchen. Most chefs will tell you that you only need a few pans and a few knives to get most things done. What follows is my list of the only 5 types of pots & pans you'll really need.
DO NOT buy non-stick teflon-coated pans. No matter what, the coating will chip and the pan will be ruined. Stainless steel is the best, IMHO. If you're preparing food the right way, you won't need non-stick anyway. Also - if you're learning & teaching yourself, just know that you will burn stuff. That just comes with the territory.
Here are few suggestions to start you off. As you get better and try new things, you'll find a need for new additions to the family.
1. Basic Stainless Steel Pan
First, buy 1 (or 2-a small & a large) good sauté pans. I've been using these two as my main cooking pans for over a decade. They're sturdy, reliable and will hold up to any punishment. You can make just about anything with these pans: Eggs, sauces, risottos, steaks, chicken, shrimp, etc. Pretty much anything. Plus they can go in the oven (something teflon CANNOT DO).
2. Boiler Pot
Next, you need a pot for boiling, simmering, & steaming: Pastas, steamed veggies, potatoes, soups, and even tamales. This will handle anything. I had a set of pots before. Once I got this, I make everything you can boil or steam in it.
3. Braiser/Dutch Oven
For our next entry, I suggest a braising pan. There are so many uses for this: Roasting, braising a whole chicken, making Mexican rice, and many other recipes. You can use it on the stovetop, in the oven, with or without the lid, and ON top of the stove it's basically a Dutch oven. There are cheaper versions, but I recommend this one. I've had it for over 15 years and still use it multiple times a week.
4. Cast Iron Pan
One item that's become a regular in the kitchen for me is a cast iron pan. They require a little more care - not as scary as it may sound, but they're worth it. With this one, you can make restaurant-quality steaks, the perfect fried egg, or even bake bread in them. You don't really use soap on them (a bit is fine, but there is a process to cleaning them properly) so they can be a bit intimidating for some. Don't let that deter you! Just look up how to care for cast iron and it will become a family heirloom for decades to come. The more you use it (season it) the better it becomes. The natural fats & oils you use when cooking will fuse with the iron to create a naturally non-stick surface - and some say amazing flavors.
Roasting pans are versatile. You can, of course, roast a turkey in this, but you can also make lasagna or roasted root vegetables. A good sized pan with a roasting rack will round out your new cookware arsenal. I've been using mine a lot lately to perfect my carnitas recipe and it's been fantastic.
The worst part about cooking for just about everyone is the last step: Cleaning up your mess. I'm a big proponent of the restaurant practice of clean-as-you-go. We were always told, "If you have time to lean, you have time to clean." It was annoying to constantly hear at first, but it was a lifesaver when it came to the end of a shift.
That's all for now. You should be able to cook just about anything with these 5 kitchen essentials. I guess I should write about essential kitchen utensils next. Till then...If you have any more questions - let me know!