i recently successfully installed osu on linux, and here are some neat tips i've collected from mostly franc[e]sco and thepoon, the two osu-on-linux professionals:
1) you can get the same latency as from wine 1.8 on recent wine versions (i've tested this on 3.5) if you use alsa and not pulse. to do this without completely removing pulse, you will need to
WINEPREFIX=whatever WINEARCH=win32 winetricks sound=alsa
WINEPREFIX=whatever WINEARCH=win32 pasuspender -- winecfg
and in the Audio tab, set the proper Output device for your system, click Apply, then Test Sound to make sure it works. Now, you can run your game with pasuspender (so for example,
WINEPREFIX=whatever WINEARCH=win32 pasuspender -- wine 'C:\\osu\osu!.exe'
) and it should work fine!
2) if you use a wacom tablet and you do not drag, you may notice that you go out of your tablet's range much easier than on windows. this is because of a tablet feature where it has two different states of being in proximity, and in range, in which the pen is still close enough that the tablet detects it but not as close as "in proximity". the current linux wacom drivers completely ignore this second state, and only update your pen's location if it's in proximity. but the maintainer of the linuxwacom project has done some work on it (i'm not sure if they're planning to merge it (perhaps as a setting) to the main driver), and
this branch is the fixed driver where you can lift your pen as high as you could on windows.
3) approach circles look weird? limit your fps.
while the game is not running, open your osu!.user.cfg, and set the CustomFrameLimit to the highest fps your computer can handle stably. Note that osu! normally shows how many milliseconds it takes to render a frame instead of the fps in the "fps counter", so the math is
fps = 1000/(how many milliseconds it takes to render one frame)