A good size, high-sided cast iron skillet and a decent sized cast iron dutch oven would be two essential items that will meet 90% of your needs when cooking on a stove or in the oven.

If you want to expand the utility a bit more, opt for an enamelled dutch oven to make it better for high-acidity dishes like tomato-based dishes.

A lightweight frying pan made of aluminium is a nice addition to this, and I'd opt for the cheapest non-stick thing you can get. It's not essential but it's a handy thing if you want to do some quick cooking or for things like crepes. Personally I have no love for non-stick cookware but especially for a home cook who is starting out it can be much easier than the alternatives.

I like Pyrex and similar glassware for its utility. The bowls can be used for all sorts of things, including baking and microwaving.

I'd recommend a good paring knife, a good santoku knife or chef's knife, and maybe a bread knife if you're big into bread (especially crusty or artisanal breads). You don't need a big knife set. I'm very partial to Kiwi knives but I hear that they are a bit pricier in the US. Here's an excellent post on knives and the discussion in the comments is worth reading too.

Steak knives are also really good (hear me out) - they're great for slicing things like ripe tomatoes and tougher foods. Not something that I'd expect would be the first thing to spring to mind for a vegan but I've been a vegetarian since forever and I use steak knives all the damn time. If you care about the edges of your cooking knives and you want to do something like slice a burger but you don't want to get another cutting board dirty, you can use steak knives to cut directly on the serving plate without feeling guilty.

A nice pepper grinder is essential imo. I do love absurd amounts of pepper so ymmv but using enough pepper is one of those things that can really elevate a dish. I like one that has a good mechanism to adjust the grind size so you can do things for texture.

This also applies to a nice salt grinder - it might be a bit me-specific but I love popcorn and I hate the ridiculous bagged stuff (that probably isn't vegan anyway). With a big pyrex bowl, something to cover the top like a plate or some cling wrap, and a bit of vegan butter you can make popcorn at home for pennies. With a nice salt grinder you can adjust it to the finest setting to make the equivalent of popcorn salt.

I like having a fish spatula on hand for dealing with delicate stuff that I'm frying and for getting under things that have developed a bit of a crust in the pan.

A heatproof rubber spatula is also invaluable. You can also get spoon-shaped spatulas that are super versatile, like this style:

I love things that make vegetable prep easier too.

The OXO handheld mandoline slicer is really good and it's probably ideal for your purposes. Definitely buy a cut resistant glove if you're going to use a mandoline though.

These julienne graters are really good too - the finer ones make really nice garnishes and it's ideal for salads and similar:

I'd strongly recommend using a cut resistant glove with this as well.

What else?

A ladle is useful, as is a stainless steel cooking spoon, and a nice broad wooden spatula.

I'd recommend investing in some nicer metal measuring cups and measuring spoons once instead of buying cheap shit.

I really like this style of measuring cups because it has internal measurements inside, so if you're making a dish that uses different cup measurements you can usually get away with only needing to dirty one measuring cup:

On a similar note, I don't think you can do better than these magnetic dual-sided measuring spoons:

They have a narrow side for getting into small containers and because they're dual-sided you sorta double up with the amount of measuring spoons you have - if one side is dirty and you need to measure out that quantity of something like salt you can just use the other end.

Rice cooker and a wok are essential for me.

You can basically cook anything in a wok, but they're best when used to make sloppy leftover stir fry with day old rice you made in the rice cooker

If you’ve got one nearby that’s open to the public, a restaurant supply store is the best place to start kitting out a kitchen. They’re cheap for the quality and will outlast equivalent priced items at big box stores, although they might not be as cute.

An 8 inch chef knife 🔪 is the standard in , and a small paring knife should cover everything you need for cutting. Other cutting tools are more nice-to-haves IMO, but a decent set of kitchen shears and a bread knife are nice.

Pick up a whisk or two, I prefer ones with handles like this

and some mixing bowls. Whisks are great for both wet and dry powder ingredients. And, while talking liquids, don’t forget a liquid measure and also some measuring cups and spoons, unless you prefer to measure exclusively by weight, for which you’ll want a scale.

The most important thing I’ll say is make sure you have a good can opener, a bottle opener, and a corkscrew. Those are things I didn’t have when I moved into my first apartment, and it sucked.

My bf spent way too much on one of those expensive hex woks, but ngl it's been pretty great and I use it basically daily.

Also an air fryer. I never anticipated how much I would use one till I got one as a gift, but not needing to preheat a big oven for small items has been a real convenience.

This bad boy is essential

Brought to you by the Swiss Army Knife company, other serrated knives do not compare

I would also recommend any large sharp kitchen knife and something to sharpen it with as this will make cutting pretty much anything so much easier, especially onions, which will make you cry less with a sharp knife, and obviously a wooden chopping board to chop things on

To begin with, you will need a flat tray for the oven, if you have one, and for the stove you will need a frying pan and a boiling pan. Probably get something cheap and nonstick to begin with, and get one big one small of each one and some cooking utensils. They come in packs so you will probs get everything you need in one go. Also recommend a rubber spatch and a wooden spoon.

By the way if you are ever wondering what ingredients to get for something like a salad or a sandwich, I highly recommend just reading the ingredients for a ready meal in the shop and just copying that.

Get yourself a good pair of tongs, and try to avoid buying anything non stick

Second the kitchen supplies suggestion, i got all my kitchen supplies from second hand stores for years

Immersion blender, very useful!

A good Santoku knife and a knife sharpener will go a long way. I have 2 cheapies and one expensive as fuck one I'm too afraid to use, and use them for almost everything. The only other knife style I'd get is a pairing knife for smaller stuff.

Get a good bread knife if you a are carb slut like me.

But other then that you really don't need any other knives.

I have one of those cheap onion choppers. Onions sting my eyes, so only having to quarter it and slap the lid 4 times to chop a whole onion is a game changer. Plus you can chop all veggies with it. I use it to dice a pound of baby carrots in under a minute. Also can be used with potatoes to get uniform cuts for fries.

use that oven a lot get some good oven safe pans and stuff. ramekins are rly helpful

Hoping I'm not to late to the party but praises for the humble electric kettle have not been sung here and that must be rectified.

A cheap electric kettle will last you for years and might become the most used appliance in your kitchen, depending on your preferences and habits. In terms of time and energy it is vastly more efficient to boil water in one of these than on a stovetop. It'll be safer (and more ergonomic) than using a microwave to boil water in an open top container such as a cup or bowl. For physics reasons, microwaving distilled water can cause it to "explode" once disturbed and kettles avoid that problem entirely.

Most people associate kettles with hot drinks and "just add water" prepared foods but any recipe that calls for boiling water can be jumpstarted by using one of these first and then transferring the water into whatever vessel you're cooking in. Beyond cooking, having quick access to hot water can be useful for things like making mop water, my apartment building has a less than stellar water heater so that may or may not be relevant to you.

Maintenance is pretty simple, keep it empty and unplug it when its not in use. Every once in a while you should descale (delime?) it by filling it up with a 1:1 mix of white vinegar and water, let it sit for a couple hours, boil it, pour it out and rinse, depending on how hard your water is you'll only have to do that once every 3-6 months, it makes a huge difference in time to boil.

Lastly, there's a lot of these nonsense all-glass ones that seem trendy right now and I would not trust normal glass to stand up to repeated heat stress like that. You should look for one that has a capacity of 1.5 to 2 liters, they're pretty resistant to wear so secondhand will be just as good as brand new. A lot of the "vintage" ones from the middle of last century are well-built and pretty cute to boot, but whether its new or second hand you're looking at the equivalent of 20-30 USD for one of these, anything more is just a ripoff.

I love my kettle :)

Honestly, my favorite tool is just a cheapo chef's knife from Ikea or somewhere like that. I occasionally sharpen it with a slab of iron and use it for like 90% of all cutting I do.

Then there are a few robots I use: a kitchen assistant with a dough hook that makes all my bread with zero hassle (it also has two more accessories that can be used for example for flax seed mayonnaise), a "multi-cooker" (like a crock pot and a rice cooker in one) that I mostly use to make rice (and if I went back in time, I'd just buy a simple cheap rice cooker instead, but oh well) and, undoubtedly, my cheapo drip coffee maker. I hate brands so I just buy slightly-above-the-cheapest stuff, good enough so it doesn't break, but that's it. 90% it's good enough. I also have a cheap bamboo steamer basket that is slightly coming apart at the seams, but it's been great for a lot of things, from spring rolls to dumplings, seitan sausage and even steaming soy beans to make milk.

Oh, honorable mention to my tortilla press, though lately I've started to just use a rolling pin as that gets the tortillas thinner than with the press.

Cast iron skillet and a dutch oven