Low Graphic Mode or Blackscreen with Nvidia GPU – Fix Guide

Update:

I have a pc with an Intel gpu onboard, which ran good for about two years.
Now I bought a Geforce GTX 1060 and when I want to start in Ubuntu 16.04 (I also have win 10 installed), I either get a blackscreen (if I try to start normal) or it loads the "low graphic mode", when I start over the failsafe mode.

I have the problem that it doesn't want to start the nvidia-driver even though I installed nvidia-375 and nvidia-settings. Here some more information:

(Is there a way to pack this whole log in a spoiler?)

Desired=Unknown/Install/Remove/Purge/Hold
| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend
|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
||/ Name Version Architecture Description
+++-==============-============-============-=================================
rc nvidia-304 304.135-0ubu amd64 NVIDIA legacy binary driver - ver
ii nvidia-375 375.66-0ubun amd64 NVIDIA binary driver - version 37
un nvidia-common none none (no description available)
un nvidia-driver- none none (no description available)
un nvidia-legacy- none none (no description available)
un nvidia-libopen none none (no description available)
un nvidia-libopen none none (no description available)
un nvidia-libopen none none (no description available)
un nvidia-opencl- none none (no description available)
rc nvidia-opencl- 304.135-0ubu amd64 NVIDIA OpenCL ICD
ii nvidia-opencl- 375.66-0ubun amd64 NVIDIA OpenCL ICD
un nvidia-persist none none (no description available)
ii nvidia-prime 0.8.2 amd64 Tools to enable NVIDIA's Prime
ii nvidia-setting 361.42-0ubun amd64 Tool for configuring the NVIDIA g
un nvidia-setting none none (no description available)
un nvidia-vdpau-d none none (no description available)

File: /var/log/Xorg.1.log

[ 27.893] (==) ModulePath set to "/usr/lib/x86_64-linux-gnu/xorg/extra-modules,/usr/lib/xorg/extra-modules,/usr/lib/xorg/modules"
[ 27.893] (II) The server relies on udev to provide the list of input devices.
If no devices become available, reconfigure udev or disable AutoAddDevices.
[ 27.897] (II) Loader magic: 0x559e2cab0dc0
[ 27.897] (II) Module ABI versions:
[ 27.897] X.Org ANSI C Emulation: 0.4
[ 27.897] X.Org Video Driver: 20.0
[ 27.897] X.Org XInput driver : 22.1
[ 27.897] X.Org Server Extension : 9.0
[ 27.898] (++) using VT number 7
[ 27.898] (II) systemd-logind: logind integration requires -keeptty and -keeptty was not provided, disabling logind integration
[ 27.898] (II) xfree86: Adding drm device (/dev/dri/card0)
[ 27.899] (--) PCI:*(0:0:2:0) 8086:0412:1458:d000 rev 6, Mem @ 0xf7800000/4194304, 0xe0000000/268435456, I/O @ 0x0000f000/64
[ 27.899] (WW) "glamoregl" will not be loaded unless you've specified it to be loaded elsewhere.
[ 27.899] (II) "glx" will be loaded by default.
[ 27.899] (II) LoadModule: "glx"
[ 27.914] (II) Loading /usr/lib/xorg/modules/extensions/libglx.so
[ 28.021] (II) Module glx: vendor="X.Org Foundation"
[ 28.021] compiled for 1.18.4, module version = 1.0.0
[ 28.021] ABI class: X.Org Server Extension, version 9.0
[ 28.021] (==) AIGLX enabled
[ 28.021] (==) Matched intel as autoconfigured driver 0
[ 28.021] (==) Matched intel as autoconfigured driver 1
[ 28.021] (==) Matched modesetting as autoconfigured driver 2
[ 28.021] (==) Matched fbdev as autoconfigured driver 3
[ 28.021] (==) Matched vesa as autoconfigured driver 4
[ 28.021] (==) Assigned the driver to the xf86ConfigLayout
[ 28.021] (II) LoadModule: "intel"
[ 28.021] (II) Loading /usr/lib/xorg/modules/drivers/intel_drv.so


Even when it would load the nvidia driver first, it says that it can't find the nvidia module.
So I think I now have two questions:
1. How can I change the 'load-order' for my drivers?
2. What are possibilities why it can't find the module 'nvidia'?

I noticed that I don't have the file /etc/X11/xorg.conf, at least not exactly named like that. My file is named xorg.conf.06252017. Does that matter?