If you’re looking for an inexpensive 2:1 to run Linux I would highly recommend the Yoga 710, 11.6″. I found an open box deal from BestBuy at $350 and eBay has plenty of them running form $300-400. For that price you get a solidly built fanless 2:1 laptop, with 4 cores, 4GB Ram and 128GB SSD.
If you go the Ubuntu route like me, don’t waste your time trying to install 16.10. According to the interwebs it’s possible but I didn’t have any luck. 17.04 however, installed without a hitch. I replaced the pre-installed Windows 10 image and now have nicely portable (2.3 lbs) laptop to cart around the house and yard for basic computing and light development.
One hint though: learn about the Novo Button before starting any OS modification. As far as I can tell easy access to the BIOS assumes restarting from that Windows 10 option. No combination of ALT, DEL or function keys will trigger the BIOS at boot. On the 710 the NOVO button is paper clip actuated and sits between the power and HDMI slot on the right side of the chassis. This seems to be a Lenovo thing, that’s not easily discoverable, but pretty handy once you realize it’s there.