Linux

I use exactly that Chromebook and here is my optimized setup after trying several options. I use it as my daily on-the-go laptop.

I run Devuan with Runit. Anything that uses SystemD is going to be too slow for this little 2 core Chromebook.

I set it up with F2FS (follow the debian howto) instead of EXT4 in an attempt to prolong the life of the little internal SSD.

I did the minimal install and then installed only Enlightenment as the desktop. You will not find a better and less resource consuming DE.

The GUI Apps:

• Terminal: Terminology
• Writing: Abiword
• Spreadsheet: Gnumeric
• Email: Thunderbird but set to leave all mail on the server and not sync any folders locally. This save the tiny SSD space and also makes it faster.
• Media: Audacious and MPV
• Web: Firefox, it runs ok but big PWAs like Gmail are very very slow.
• Smolweb: Bombadillo, but everything else works great too.
• Network: ConnMan, this is all you need, no dhcpcd etc to manage network/wifi connections, and there is a nice simple GUI "gadget" for it included with Enlightenment

I love this specific chromebook, I have the blue and white one, its keyboard is so much better than it should be for the price.

I keep a 128G EXT4 sd card mounted at /home//data and I replace dirs that get a lot of use like ~/Downloads with a symlink to the sd card.

You can squeeze a little more juice out of the CPU by changing the default kernel command line to include turning off all the CPU security mitigations. You don't need them on a single user chromebook anyway.

edit: formatting

eta: I forgot to mention that I also mapped all the top row keys onto functions in Enlightenment so they do what you expect them to do.

eta: ConnMan