After trying out a few distributions I stopped at Xubuntu, so far it seems to work better than Ubuntu Unity and BunsenLabs (Debian with Openbox).
The thing with the latter two is that the rotated display performed very poorly -- the refresh rate was close to 2-3hz. Even something as simple as moving application windows created a LOT of tearing. Gaming performance was poor as well (I used Owlboy as a quick and very lenient benchmark -- on Ubuntu it struggled at ~20fps). At the same time, with non-rotated (vertical) screen everything was fine. On ubuntu the slowdown happened after I disabled 3d acceleration in xorg.conf (Option "DRI" "False") to stop crashes; after that compton was hogging all of the CPU time, probably because it had to go with software compositing.
What happened on BunsenLabs is a mystery -- there I didn't disable 3d acceleration, and I tried to disable to compositor but nothing really helped the performance.
It is not implausible that some compositors don't like rotated screens and gnome's mutter may be at fault for the poor gaming performance (but I have no idea what I'm talking about here). Piece_Maker, you might want to try out other distros to be sure.
UPD: tried Rocket League on xfce, it's pretty slow as well. So it's probably an issue with the port itself.
Bluetooth seems to work with Matan's solution (I had to additionally install pulseaudio-modules-bluetooth to use my bluetooth headphones, but that's not specific to GPD Win).
The only thing not working so far is the microSD reader and I haven't tested the microphone. But everything else seems shiny after what little testing I performed.
UPD Jun 20: nope, not shiny, it's still crashing pretty heavily in games. All games crash the same way: within a couple of minutes of playing the screen freezes and the last 2-3 sec of sound are playing on a loop, -- so that's a problem with the system, not the games.
-- Disabling CPU Turbo Mode in BIOS as Arch wiki suggests had no effect;
-- using kernel option "intel_idle.max_cstate=1" as per this bug
had no effect;
-- using xorg option "DRI" "False" to disable 3d acceleration helped -- I was able to play through 20min of Papers Please without crashing, -- but renders any 3d games unplayable, which is not really a tolerable outcome.
Has anyone figured this part out?
UPD: kernel boot option "i915.enable_rc6=0" helped.