If you've relatively new to Linux installation or you're not well versed to, or would rather not, compile from source or mess with config files often, I wouldn't recommend you start with Arch. Once you're ready to learn on a more manual system, Arch is your frienenemy.

I usually recommend Linux Mint (Cinnamon) for those coming from Windows or Ubuntu Budgie for those coming from Mac, but those two may be too hardware intensive for the Chromebook.

Look here to get started with lightweight distros. I've used all of them, and they all have their pros and cons, but are all worth checking out as daily drivers. To put it in perspective, I have antiX running on an IBM ThinkPad T20 with 256mb of RAM, and it's running as smooth as butter. The other day, I even ran a modern USB mouse with 0 issues and 0 wait (whereas Win10 spent a good minute or two installing drivers before I could use the mouse).

Another great starting point is Distro Chooser.