I like to have a few good quality multi-use items. For example, and nice chef’s knife will crush garlic perfectly well and still cut your veggies. My list of essentials:
Three stainless-steel pots (small, medium, large) with the thickest bottoms you can afford.
A couple of frying pans, at least one large. I personally hate non-stick frying pans because of the chemicals they can give off and the way they wear out even if treated with kid gloves. I LOVE my cast iron. It cooks better, is healthier, and you can use stainless steel utensils.
About utensils: Mine are mostly vintage/ antique hand-me-downs. I LOVE them- the spatulas especially. If you can find nice, springy but still firm steel spatulas, get them. The last thing you want to happen when you’re flipping a fish filet or burger is to have the spatula give way and dump your food. I’ve never found a plastic one that I like. My ultimate utensil list: 1 spatula, 1 stainless steel ladle for soups, assorted wooden spoons (they’re cheap, so I usually throw mine out if I think there’s something growing in it), tongs, and a whisk. Obviously other utensils can be added, but you can cook just about anything with the above items.
I like glass (Pyrex) mixing bowls. If I’m whisking, beating, stirring, etc., they’re heavy enough to stay still better than steel.
Knives: I only have three. A very good (and very old) chef’s knife, a decent paring knife, and a filet knife. They serve me well. If you don’t want to be constantly washing them, more is better, but you don’t necessarily need any more than 2 or 3 knives even if you do a lot of cooking. I cook every single day- and it’s all from scratch.
A couple baking sheets and some pyrex baking pans/ casserole dishes are super useful.
I like to have two cutting boards- one for meat, and one for vegetables. The meat cutting board is plastic so I can be sure to kill all the germs. I try to be very careful when it comes to avoiding cross contamination.
I lived for a long time without a food processor or blender; they aren’t that important in the foods that I cook. An inexpensive alternative is a food mill. You can only run mushy foods through it, though; boiling will make most things mushy. I mostly use it for applesauce and potatoe soup.
I don’t cook or bake with thermometers except for an oven thermometer. It takes a lot of practice to tell when food is done properly, so if you’re new to cooking, probe thermometers are a lifesaver.
Measuring cups and spoons are useful for baking. So is a rolling pin, and various other baking pans.
That’s pretty much my kitchen! It’s horribly long, I know. I’ve found a system that works well for me; if you cook differently, my system might not work so well for you. I hope this helps:)