Anything in the *80 series or newer is WELL worth the extra money. *70s and below are typically dual cores unless you get high end "workstation" tier machines. Dual cores are usable, but quad core machines are really the bare minimum you want for a truly good experience dealing with the modern web.
My preference is generally to stick with the X and T series of machines. W and P series carry a premium because they're the highest end workstations (I do love my P1, but that was almost 4k USD). T4XX and T14 are the most common models you'll see used, but the T5XX and T15/T16 machines are less common, but also less in demand so they can be cheaper. There is the P15s/P16s which are literally just their T series counterparts, just with an ISV certification, and quadro video cards instead of geforce.
I'd also HIGHLY suggest avoiding "refurbished" machines. You're paying a premium for someone to wipe the computer down for you. They're not replacing any parts, you're just getting a used computer. The only refurbished machines I'd buy are straight from the manufacturer. And you're buying a ThinkPad so a warranty shouldn't be needed. As long as it works when you get it, it should only fail if you broke it.
Finally actual model advice. The T480 is the first machine with a quadcore CPU, but also the last (until lately) with 2 ram slots. It's also the oldest machine to natively support windows 11. Irrelevant to you, but relevant to the price of the machine. At least in the US most ThinkPads bottom out at about $200 (USD) and only dip below that if they're broken or too old to run windows 11. The T490 is the exact same thing, but only 1 socketed ram slot and the other half of the ram is soldered, but they're MUCH cheaper. I got a T14 Gen. 1 about 2 years ago for $200 USD, and about a year ago I got a T14 gen 3 for $250. Don't be afraid to look newer, they might be cheaper. T490 and T14 gen 1 might just be close enough to your price range.
Also if you can try looking on local classified ads. Prices online will almost always be higher because the marketplace takes a cut of the sales price. I only get good deals on Facebook Marketplace, and Craigslist. I'm not sure what's popular in your area, but try that.
