I would try Fedora 28, or if you are a bit more technical- Arch. I'm running Arch on a 13" and it works flawlessly. I've had a lot better experiences using Fedora when compared to Ubuntu.
If you want to use Arch but are not that hardcore-technical (command line installer etc.), try Antergos. It's like Arch ez-mode -- GUI installer, installs with a GUI of your choice (Gnome by default), uses all the Arch packages. I am running Antergos on a Lenovo Ideapad 720s and it's a pleasant experience.