That's a hard one... the first two things I thought of were the Pinebook and the Pi-top, but both seem to have been discontinued and the latter was out of budget anyway.

I guess I'd go on eBay, get something used for around $50-100, slap Debian LXDE, Q4OS Trinity, or AntiX on it, and see what I could do in terms of repairs and upgrades for the rest of the budget. I'd be interested in a ThinkPad that supports libreboot, or something from the netbook era like an Asus EeePC, but if I needed to use it as my main laptop I'd probably try to find something from the Windows 8 era instead.