I’m assuming you have a kitchen supplied with basic cooking equipment like pots and pans with lids, a few Pyrex baking dishes, measuring cups and spoons, spatulas, wooden spoons, whisks, a can opener, etc. There are so many kitchen gadgets you can buy, and I have some of them, but for most cooking, these basic items form a good start.
If you have non-stick pans, especially old ones, please discard them. Nonstick coating is a toxic no-no. The Environmental Working Group recommends you use stainless or cast iron cookware to avoid potential problems with new chemicals used in nonstick cookware.
Likewise for aluminum pans, which can leach aluminum into food. If you have aluminum pans, get rid of them. (Even anodized aluminum, if scratched, can leach aluminum.) Research into the effect of aluminum exposure on human health is mixed, but my philosophy is “when in doubt, leave it out.” Toss (or recycle) those pans.
Ceramic pans are best, followed by stainless steel, which I use. Some people swear by seasoned cast iron pans, but I don’t use them because I don’t want any extra iron in my food. Le Creuset lead-free enameled cast-iron pans are great, if you can afford them. I cook with stainless steel pans (I bought mine at Costco). Stainless steel leaches nickel and chromium into foods, so I use wood utensils as much as possible to avoid scratching the stainless steel. Eventually, I’ll replace my stainless cookware with ceramic pans or, if I win the lottery, with Le Creuset.
I cook on an electric cooktop and use an electric oven because there’s no gas in my area. I prefer gas, but I do just fine with electric. If you can cook, you can cook over a Bunsen burner if you have to. I also have a Cobb grill, which I love, for outdoor grilling. Whatever source of heat you have will work if you know how to use it.
I don’t have a microwave oven. Most microwave ovens leak radiation. You can test to see if yours leaks by putting your cell phone inside it (don’t turn the microwave on) and calling it. If the phone rings, your oven leaks. I have a toaster oven, which heats food almost as fast as a microwave does. I heat up cold coffee in my toaster oven. It gets plenty hot and tastes fine.
I have a Vitamix blender, a Kitchen Aid stand mixer, a Kitchen Aid stick blender, a Cuisinart ice cream maker and a Cuisinart food processor. The Vitamix is expensive, but it’s fabulous for smoothies, which we drink all summer and well into the winter. If you can’t afford a Vitamix, get a good blender. I had a $30 Oster blender for years that worked fine. The ice cream maker was a gift, and I use it on occasion. I bought a juicer long ago, but it’s in the basement now. I used it a few times, but it was hard to clean and seemed to waste all that good pulp. The Vitamix pulverizes all the pulp, so you can drink it down, which seems a lot healthier to me. Fiber is good for you, so why waste it?
The stick blender is not essential, but it’s very helpful for making soups. The food processor is useful for making nut butters or pulverizing crackers or bread into gluten-free crumbs or breading. I use the Vitamix more often for chopping and pulverizing. The stand mixer is so much easier than a hand mixer. I don’t think I could bake without it. I bought mine on sale at Target about 20 years ago, and it’s still going strong. It’s a great, essential appliance if you plan on doing any baking.