Can't go wrong with a used T series from Ebay that's a couple years old. A quick search shows that you can get something like this for 320USD from a reputable seller:

Lenovo Thinkpad T14 Ryzen 5 Pro 4650U 2.10 GHz with Radeon Graphics 16GB 256GB

8GB is too little RAM these days otherwise I would also recommend the X13 model but those start at like 600USD for the 16GB models.

T480 if you can find it around that price. Or any Thinkpad with 8th generation Intel CPU. (L380, X380)

I second the idea of a T480, it’s what I use. I threw Linux Mint on it and never even think about it, but if you want to use Windows, then I see no reason why it wouldn’t run perfectly well either. Looks like they go for $120-200usd depending on configuration. I spent over $300 a year and a half ago, and I would still consider that a good deal, so $200 is a bargain imo.

I want to buy a thinkpad that I can set up as a privacy machine

The older ThinkPads can go much further in the freedom/privacy realm than new ones. If you think you'd want to set up a custom BIOS etc., look at T440. There's also T430 but it doesn't support 4K output on external monitors. But you said you're not "especially tech-literate", so I assume you're more towards the newer ones.

The video below makes the point "old but modifiable" vs "new and fast" https://www.youtube.com/watch?v=y2OB6zfL904

I bought both my parents new old machines now that they retired, and I opted for a T480 for both. They've been called The Last Great ThinkPad over on r/thinkpad since they are both powerful - first generation with a quad-core processor - and nicely upgradable. The upgradeability also means that you don't have to worry overly about the amount of RAM a used model has: you can always add more cheaply (and very easily).

I think the T480 is a great deal but be aware of the Thunderbolt firmware issues. It’s fixable if the firmware is not yet fully corrupted and if the firmware is up to date it shouldn’t be a problem, but I’m dealing with a dead thunderbolt chip on mine right now and it’s terrible