It's absolutely imperative to begin with a sturdy chef's knife and cutting board, and a few of my recommendations are below. Beyond that, a good set of pots and pans, a heavy cast iron skillet, and basic utensils like wooden spoons, rubber and metal spatula, and tongs make kitchen tasks easy.
Chef's Knife - The two leading manufacturers of chef's knifes are Wusthof and Henckels, and I happen to have a couple of each. I prefer mine in an 8" size, but you can also get 6" all the way up to 12". You can get a good, sturdy knife that is fairly lightweight and stays sharp for about $50-100. I like Wusthof's 8" Gourmet Chef's Knife. A Sharpening Steel is usually another $20-30, and a diamond blade sharpener is about $30-50 more. I use my Chef's Choice Manual Knife Sharpener at least once a month since I'm cutting and chopping every day.
Cutting Board - My one rule for cutting boards is NEVER buy a glass one. My second rule is NEVER buy a flexible plastic one. Unless you want to dull your knife every time you use it or slip and cut yourself, you're better off using a hardwood board that can be cleaned with natural cleaners and sealed with mineral oil. The bigger the better, too, especially if you're cutting a ton of veggies. Chef's Catalogue has a gorgeous 18" square butcher block board for just under $90. Catskill Butcher Block Cutting Board - MEDIUM 18" SQUARE
Cast Iron Skillet - The Lodge is the maker of my "go to" pan in 10" or 12", which goes from stovetop to oven and works great for tofu frittata, cornbread, and even pizza. Depending on desired size, you can purchase the Lodge Logic Cast Iron Skillet for around $20-40. You can even get one just for making cornbread.
Cookware - Everyone needs a good set of pots and pans. I'd recommend a stainless steel or hard anodized set that includes a minimum of a 6-quart stock pot, 10" frying pan, sautee pan, and 2-quart sauce pot with covers, preferably with handles that stay cool while cooking and that are oven safe. If you really want to splurge, you can't go wrong with All-Clad. It's practically indestructible, heats quickly and evenly, and holds heat well. The only negative is that it's EXTREMELY heavy, so don't plan on carrying it around with you in your backpack! ABT is running a great special right now on a 9-piece set that includes all of the above pieces for just under $660. A bargain! All-Clad 9 Piece Stainless Steel Cookware Set
Mixing Bowls - Any baker needs an ample supply of mixing bowls. I like the glass or stainless steel variety that are of different sizes and nest comfortably together on the shelf, like these from Chef's Catalogue CHEFS Stainless-Steel Mixing Bowls. I also like pretty ceramic sets and melamine, all of which work well and make mixing things up in the kitchen tons of fun. Kohl's has some cute and colorful ones from Rachael Ray, KitchenAid, and Food Network. There's even a 5-quart collapsible mixing bowl for those tight on space, appropriately named, Squish.
Baking Dishes - I'm tempted to just recommend going to your local thrift store for some classic Pyrex, Fire King, and Corningware, because that's where you'll find all the good stuff. But you can also get some pretty ovenproof ceramic bakeware in places like Williams Sonoma, Pottery Barn or Crate and Barrel. And why not get fancy with some Le Creuset Classic Stoneware or Emile Henry Olive Oval Gratin since it's the holidays after all? I kinda like this flame top Tagine, and I'd probably try a bunch of new recipes just so I could use it every day for about a month.
Trivet - The last kitchen essential is something to put those hot pots and baking dishes on. But don't just look at this item as utilitarian! This is an opportunity to add some personality to the chef's kitchen, and every time they place dinner on this handy little fella, they think of you, too. I generally look for indestructible cast iron, but Kohl's has this really cute 2-piece trivet set in environmentally friendly bamboo. That would look lovely on any kitchen table.
Next.... what equipment does every chef need? I'll tell you more tomorrow!