The HP Envy 13z is a lightweight, reasonably high-performance laptop with a relatively low price tag - under $600 for the 1080P 13" touchscreen, flip-hinge to tablet, backlit keyboard, 8GB RAM, 250GB SSD, Ryzen 2300U four-core system weighing a little over two pounds.
(Those were the specs.)
It generally compares favorably to a non-Retina MacBook Pro.
Unsurprisingly, it ships with Windows 10 and HP support wants nothing to do with Linux. Honestly, if they just changed their stock answer away from hostility to polite indifference, it would be a remarkable improvement. Running Windows disk management utility produced a 112GB partition for Linux to use.
Important safety tip: you need to reboot, hit ESC a bunch of times until the BIOS menu shows up, and go into the BIOS settings to enable Legacy Boot (and thus turn off Secure Boot). Then you can boot from a Linux USB installer.
If your chosen distro is not bleeding-edge, you will want a working USB-ethernet adapter. You’ll need Linux kernel 4.18 or later, a recent firmware package for an RTL8820be (r8822be is the module name), and a recent Xorg release for amdgpu. There is currently no support for the touchscreen, but it looks like that will be supported in the nearish future. The camera works immediately, as does sound.
It took me about 4.5 hours to go from unboxing to a reasonable dual-boot. It would be perhaps an hour if I didn’t need to research anything.
March 2020 update ~~~~~~~~~~~~~~~~~
Upgrading to Debian buster and using the buster-backports kernel:
apt install -t buster-backports linux-image-amd64
gets you a working touchscreen. At this point, everything on the box works.
You may want an xrandr alias to rotate the screen 180 degrees for times that you hinge the screen over into tablet mode.