If you are looking for a cheap small laptop with good Linux compatibility and decent specs, I certainly support your search for a chromebook to use as a platform.
However, I am typing this from a refurb Lenovo X380 which was 1200+ when new a few years back, but which I picked up for around 200 bucks a year-ish ago. I have manjaro on it, and it's flawless. Comfy keyboard, pretty good specs, great looking 1080p display.
I liked it so much I talked my mom into getting one when she was on a similar quest recently. She lives too far away for me to push her out of her comfort zone, so she's running Windows on it, but even with Win10 it's a pretty good performer for typical tasks.
I love the darn thing - apologies if I've misread your goal though.
They now have the 16GB model avail for about what I paid for the 8GB model. (And the seller I bought the 8GB model from is charging more for it than for this 16GB model, oddly)