Since you are explicitly asking for cheapest: a used Motorola Moto G7 Play can be gotten very cheap. Alternatively, a used Pixel 3a. You probably find something cheaper from Xiaomi, but I'd stay clear as unlocking the bootloader is not pleasant on these devices.
Personally, I would aim a little higher though. I run it on a Pixel 4a and am quite happy. (Don't get the Pixel 4/XL since those do not have a fingerprint reader but only Face Unlock, which the latest LineageOS does not support.)
I tried looking for these phones on eBay - it’s a bit challenging to find unlocked refurbished phone that would work in my region from a trusted seller. Sometimes you have to take the leap of faith with a purchase and hope it works. It’s a bit of a headache…
That's a good tip. I've got a moto g32 (ca. 130 € new) running LineageOS and am happy with it. Only downside is the CPU which could be a tad faster.
Unlocking the phone's bootloader is also not so easy, because you have to register your phone online and the web page is quite finicky. I had to try with different browsers to get the registration form to work.
Yeah, Motorola (which are now a brand of Lenovo after Google bought and sold them a while ago) are good value for money. I owned the Motorola Milestone (Motorola Droid in the US), then the Moto X (smaller version of the Nexus 6), and finally the ultra-thin Moto Z - however I was a bit disappointed with that one because the battery management was totally screwed up after a few years - it used to shut down spontaneously while reporting 60% battery and I wasn't able to reset it.