I’m sure I’ll forget some things, and I haven’t read through all the other posts.
Basic are a cast iron skillet that can go from stove to oven (yes, they require maintenance, but there are tons of guides out there on the web), and a non-stick skillet, a saucepan and a big pot for cooking pasta with steam attachments. A cookie sheet and a muffin tin, and round and/or square ceramic or pyrex casserole dish (preferably with lid), and a loaf pan.
Mixing bowls and colanders. A box grater (microplanes are nice, but I don’t see that as a necessity for a beginner, since some of the box graters have decent fine grate sides that can handle parmesan, citrus zest, ginger and garlic). A large spice rack. Measuring cups and spoons.
GOOD KNIVES. You don’t need a ton, but you need them to be good. They also have to feel right in the hand. We have a great santoku that my gourmand fiancĂ© loves, but it was too big for me, so we got the smaller version for me. A paring knife, and bread knife, a Chef’s knife and a carving knife are a good starting point. The smaller blocks usually have the essentials and include steak knives and a sharpener, which is nice. You’re better off paying for a smaller, high quality knife set that a larger, lower quality set.
I like bamboo utensils instead of wood, and you need some nylon/silicone ones, too: slotted spoon, large spoon, spatula, whisk, tongs, can opener, bottle opener, ladle, pie server. We have several sets of tongs, as those get a whole lot of use in our kitchen.
As for appliances, a microwave and coffeemaker (if they drink coffee). A toaster or a toaster oven—if they live alone, a lot of items can be cooked or re-heated in the toaster oven so you don’t have to waste the energy of heating the whole oven. Most serious chefs I know think very poorly of crock pots, and instead suggest pressure cookers (many of which can be used as rice cookers and steamers, also). A kettle for boiling water for tea and such. We love our electric grill/skillet, and use that more than the toaster and microwave. I love how the grease drains on the grill side, so we make our bacon, and sausages and I even re-heat pizza on there (ours has adjustable settings for the top plate, so you won’t touch the cheese or over pressurize your paninis. The top opens flat and the grates flip to a smooth griddle setting that’s terrific for pancakes and similar items.
I can’t even remember the last time I used a hand mixer. Most stuff I do with a whisk, the stick blender. We went for a few years without a regular blender, and we really don’t use it much. There are a few multi-functional appliances out there, to help conserve counter space and expense of having multiple devices. So I don’t think that these are essential; but as a person evolves and finds themselves encountering recipes that call for one type of appliance more often than others, it’s worth adding that to their collection.