For a cheap laptop, you probably want a used model. A refurb will be cheaper than a new one, but a used one will be cheaper yet. Ideally you’ll buy from somewhere you can try it out, or where you can return it without an argument if it turns out to be no good.
A local supplier might be a good bet, especially if you’ve heard a recommendation.
Personally, I’ve bought refurb Macbooks, twice, which are pretty pricey but I like the quality. And I’ve bought a refurb Chromebook, once, which turned out to have a poor keyboard. With either of those, they come with an operating system which is pretty safe and reliable and usually automatically updated.
With any other laptop, you’re probably going to want to run Windows or Linux. I know very little about Windows these days - it keeps moving on, and my knowledge isn’t up to date. But I know a bit about Linux, and I’d recommend it to anyone who doesn’t have very specific needs (like running particular software which only runs on Windows, or being not at all confident of running an unfamiliar operating system.)
There are many Linux distributions to choose from (Ubuntu is a safe choice) and you can experiment before you settle on one, but one thing you will want is compatibility with your laptop’s hardware. I once bought a Toshiba laptop and the wifi worked perfectly well with Windows but didn’t work at all with Linux.
Here’s a place to check compatibility: LinLap
As for hardware specs, having enough RAM is the primary thing: 4G is good, 8G is better. If the machine comes with 4G but you know it can be upgraded to 8G that’s fine too. I’ve previously bought memory from Crucial. Similarly if a machine comes with 2G but can upgrade to 4G, that might be OK.
If you have the money to fit a solid state disk (SSD) that will improve the responsiveness and the robustness of the laptop. With no moving parts, it should be quieter, cooler, and more likely to survive a drop. I see Crucial sell SSDs too.
As a worked example, I see at Morgan they have a number of Dell Latitude E6410 and Lenovo Thinkpad T410. Both are respectable brands. I notice some of the Thinkpads are described as having no webcam - that might be what you want (for privacy) or it might be what you don’t want (because you want to do video calling.) Checking at LinLap, I see the Thinkpad is mostly rated ‘excellent’ for Linux, and can be upgraded to 4G RAM. The E6410 has less detail but users report no problem at all.