Got the game running without modifying anything setup-wise and it was ok, so if you're ok with that, don't change anything.
Setup:
Debian Jessie x64 with the necessary x32 libraries
Crossover 15.0.1
Two monitors, each with a resolution of 1920x1200
Nvidia GTX 970 using proprietary driver version 352.79-1~bpo8+1
I determined that the following contents of hitman.ini worked the best for me. The file is located here, if you haven't changed the installation folder:
c:/Program Files/Steam/steamapps/common/Hitman Codename 47/hitman.ini
My hitman.ini settings:
Include Setup\Locale.zip
//DrawDll Render3DFX.dll
//DrawDll renderd3d.dll
DrawDll RenderOpenGL.dll
SoundDll Sound.dll
ScriptDll GSC.dll
LocaleDLL Locale.dll
Resolution 1280x1024
//enableconsole
StartUpperPos 320,50
ColorDepth 32
Anisotropy 2
DisableLight
ShadowDetail 2
TextureResolution 0
WindowIt doesn't seem to matter, to me at least which of the three renderers I used, so I chose OpenGL.
I set the game to windowed mode, as I didn't like it in fullscreen, as fullscreen seemed to squeeze the image regardless of the different resolutions I chose.
So I set the resolution to something lower than my monitor's resolution, and finally I set the StartUpperPos as I'm using two monitors, as I want it to be located in the center of the left monitor. My monitor resolution is 1920x1200 so if yours is different, you'll need to use trial and error to determine the correct values of the offsets for StartUpperPos.
I found inspiration for most of the settings, in this article: http://www.pcgamer.com/pixel-boost-hitman-codename-47-at-4k/
The first of only two problems I haven't been able to solve, is that the sound becomes delayed for 0,5 second for some reason. It seems to be related to certain types of sounds from the game, that will trigger this permanent delay of the sound, until the next restart of the game exe-file.
The second problem, is the map, that will behave annoyingly when zooming in and out, as well as when switching between the layers. It will sometimes not use the mouse cursor as the center of the zoom action, so you will zoom in/out on a completely different part of the map, and will then afterwards have to manually move the map to the point you were interested in. Also the map is not completely accurate in displaying your position on the map, but it should be fairly easy to determine the precise location.