Just get a cheap Chromebook and install GalliumOS on it. Its a lightweight distro specifically for Chromebooks.
I got myself an Acer CB3-431 a few years back and did just that. Full metal body, 14 inch screen and some random Intel dual core SoC for £200ish. The distro and SDD make it feel pretty nippy considering the hardware and the battery lasts 10+ hours with heavy use (I mostly use it for coding and web browsing).
It's pretty much what I always wanted netbooks to be but never were.