We always do a bunch of price comparisons quickly! IKEA is definitely a good one for some stuff like coffee tables/end tables and housewares but I do find for other things still a bit pricey and you can find better deals elsewhere.
My main checks for furniture and stuff are IKEA, Amazon, and Ebay and then comparing them to my local "Car Boot" page on Facebook. You can also physically go to car boot sales when they're on or check out charity shops (British Heart Foundation I think was mentioned and they're a good one to get furniture at if you have one of their shops near you). With things that are less of a priority but are more expensive, just slowly save up and buy them when you see a good offer on at the shops/when you've had time to save. In addition to car boot care pages on Facebook, there's the Facebook marketplace and there are other local "free" pages where they will be giving things away for free but sometimes it requires you to have contributed before taking so you just need to check out the pages rules. Other than those, there's an app called Shpock that's a car boot sale type app. I've purchased shoes from it before but they do have all kinds of stuff. Gumtree is an option but I always find that there's nothing really good or worthwhile near me so I just stopped using it.
That's all where to look for things you're buying, as far as *what* to bring vs buy, I would agree that good pairs of jeans/trousers are definitely worth taking as it can be reallly hard to find ones that fit you right (when you find a pair that fit you right, buy them all!). If you want a flat sheet for your bed, those are trickier to find so I would bring those but I find I've had no problem replacing towels with IKEA towels for cheap as well as finding cheap fitted sheets for the bed (although, as others mentioned, that may vary if you bring your own bed from home).
I personally prioritised taking things that were more personal like photo albums and collectables so that I'd feel more at home. My philosophy was that over time, I could replace any appliances/furniture as needed but those personal and sentimental items could *only* be had if I brought them with me. If I went back in time now, I'd probably even pack less clothes (I would've left some back at my parent's house so I could bring less over when I visit them!) and just less in general as I found that my husband's flat was just too small for all my items to fit nicely so the place just looked cluttered for a while (since moving, it all fits nicely more or less haha). So yeah, I would be packing things you definitely can't get here (like certain foods or sentimental items) and things that will be too much of a pain or too expensive to replace (like flat sheets or a laptop) and just slowly replacing the rest by importance once you get over here and can see how much space you have/what you need. Also, I forgot, Argos is a good one for some appliances so it might be a good place to go for blowdryers/ete although you might find them cheaper on Amazon (it's all just a big comparison game if you have the patience!).