A toaster!

I always suggest a decent sized rug/runner. Not only do they help tie together a room/hallway/entrance/etc in general, but they also help dampen noise. For example, when I moved into my current apartment - even with all my furniture and a bunch of stuff on the walls, walking around barefoot would echo really badly and god forbid I turned the AC on because the fan noise would echo. A rug and matching runner I got from the thrift store for $50 solved that and as a bonus, I can walk around barefoot without my feet getting cold from the hardwood

If you're into it plants can make really nice cheap decorations and add a feel of life to the place.

If you don't have pets then indoor plants are good fun. A fair bit if upkeep but look really nice, really liked mine made the place feel more alive.

Couldn't hurt to have a first aid kit

Anyway time for our indoor plants vs outdoor plants struggle sesh

Have you considered using a bunch of empty liquor bottles as decoration? An empty bottle of Jameson on a mantle or on a windowsill has a je ne sais quoi that well put together apartments rarely have.

Doubly so if you don't actually drink.

Next time I move into my own place, I am aiming to have a framed picture of Josip Tito next to an empty bottle of Tito's Handmade Vodka somewhere visible but not prominent as an irl visual gag.

I echo all the art-on-the-walls suggestions. even blank canvases can be something if you think you might later paint on them. but there's plenty of secondhand shit for the walls all over. you can also hang fabric on walls to create warmth and patterns. I like hanging fabric on doorways and in hallways too, to pass through, because I am a weirdo and like to articulate the visual field to define spaces. people usually furrow their brow at it unless they are also weird like me and then they sort of laugh when they pass through.

also, depending on the floor situation, rugs are cool. usually one at the entry door(s), one in the bathroom, one for the kitchen, and something for the living area.

This may depend on personal preference and your shoe/carpet policy, but if you like sitting on the floor/sitting at a low coffee table you can get floor cushions. I got four or so from Daiso (called zabuton) in alternating colours. They add colour to a space that's often unoccupied and make the floor a bit more cosy

Rice cooker, for sure.

Get good sheets.

It’s been mentioned already, but good knives for the kitchen.

consider a rug

Get some blankets and cushions - makes sitting on the sofa so much more cozy if the room is cold. Also a hot water bottle is amazing for this and for cold beds too! If you’re a shoes off in the home kinda person (which you should be - the streets are dirty!) then get some good warm slippers. A lifesaver if you’re running the place a bit colder.

Dehumidifier’s are really good but they’re expensive to run, and don’t forget to ventilate - open the windows daily.

Something every residence should have is Carbon Monoxide and smoke alarms - they are not expensive and may save your life. Also a small fire extinguisher and fire blanket.

It’s nerd shit, but running some type of mini pc or raspberry pi with pihole for adblocking and some type of jellyfin and arr stack if you’re inclined is very good for media.

Get an aeropress. I’m also a big fan of a Moka pot.

Tools: the most important ones are a decent measuring tape, a claw hammer, some pozidrive and flathead screwdrivers (or whatever your local fixings tend to be: torx, Allen, square etc), for hanging pictures and the like get a torpedo spirit level, they don’t take much space. Buy cheap tools - if they wear out or are insufficient only then buy good quality ones. The fact is if you don’t do much work the $2 claw hammer you bought at Walmart may be all you ever need, and that’s better than spending $100+ on a pro framing hammer that you’ll never see the benefit of. Then beyond those basic hand tools, a Combi drill with hammer functionality is very useful. After that only get the tools you need, for the tasks you intend to do. No point owning a circular saw if you’re never planning on cutting a load of timber or a pipe cutter if you never do any plumbing!

Also buy a torch incase of power cuts and store it somewhere you can find it in the dark!

This is left of field, but I’ve got an ancient 80s era Braun analog alarm clock (other alarm clocks will also be perfect) that I keep by my bed so I can still wake up but also not have my phone in the bedroom. I strongly recommend it. Phones in the bedroom are a route to late night scrolling and ignoring your partner. Not good. It’s a thief of romance and time.

Easy to care for plants, like golden porthos, ZZ plants, etc. Or, even tasteful fake plants for those no light areas like bathrooms without windows.

I second buying thrift store art, keep in mind, you might buy a few that you end up not showing/displaying, ok to redonate.

Also, two huge things to help keep your place neat is to make sure every item has a home, and more cabinet/covered storage is good, for example, buy furniture that has drawers, like beside tables, coffee tables with drawers, couch side tables with drawers, etc.

I have large magnet marker board on my fridge that I use all the time, you could also get a nice wall corkboard, or even paint a wall with "black slate" paint so that you can write on it with chalk. Also good to have a filebox with hanging folders and use it to keep papers organized, and have a system for your mail so it isn't sitting around.

Oh and if you have a place to compost, use a coffee canister for food scraps. Food in the compost, rinse off anything with food residue. If you have this, plus a nearby place to recycle stuff, your trash won't stink, and you won't go through as many trash bags.

Congrats on your new place 🛖 I'd like to suggest lamps if you don't have them. Both table and floor. Overhead lighting sucks eggs. Speaking of, if you like them, hard boiled eggs are the the easiest yummiest snack to keep on hand. Let's see. Throw rugs. Ottoman. Putting a towel under your cutting board keeps it from sliding. Meet your neighbors and bake them some cookies if they seem nice.

I agree with plants. Definitely at least some succulents. You can leave a cactus in the bathroom and never water it because it'll absorb moisture from steam.

Warm coloured lamps, adjustable, or non adjustable but placed so your lighting can always match the mood.

Nice pair of speakers, if that's your thing.

Disagree with what people are saying about art. Yes, get some art, but don't rush it. Buy what really appeals to you. Don't just get random shit for the sake of filling your walls.

Manual food processor. Chops and onion (or anything else) in 2 seconds. Doesn't need to be plugged in. Costs 10 quid. Cleans out as easily as cleaning a bowl.

Couple fridge magnets?

The entire works of Lenin. No but seriously, a nice wooden bookshelf with a nicely assorted set of books.

General bric a brac. I now buy really tacky mini sculptures of British Wildlife whenever I see them in charity shops, and I put them all over the house.

Homemade stuff, if you like crafts. I made a funny weed box, where it looks like Agent Cooper from twin peaks is handing you a blunt.

I'd agree with all of your suggestions, except maybe the cold brew maker. I've found using a french press works pretty much just as well and you can make hot coffee in it too!
The real curveball, that honestly might be unnecessary, is a new shower head. My last place had an awful one, it would push out a ton of water really haphazardly. The QoL upgrade when I finally (after 1.5 years of suffering) bought and installed my own was kind of upsetting. I got better pressure, better coverage, and the hot water lasted longer since it was using less. For $20 and a few minutes of install my life got so much better. And if you have the ceiling space, I think an extender isn't a bad idea either: you can sort of get the "waterfall" effect without splurging on a high end showerhead.

House plants if you have any natural light.

This is a bit more of a commitment but I really liked keeping a fishtank in my first apartment that didn't get enough natural light for pants in the living room.

For coffee you might look at an Aeropress, if you're only making one cup at a time. Cheap, reasonably durable, and make some of the best coffee I've ever had.