Ubuntu won't be installed after many attempts

[Shakib Molavi]

Hi
As I'm new to Linux, I have tried to install Ubuntu many times, but every time I have faced with a new error message or a misbehaviour.
Last time that I tried, everything went well, OS was installed, but after reboot when the bootable-usb was mounted, it took me to the installation page (Try Ubuntu, Install Ubuntu, OEM installation & disk check-up) AND when usb was unmounted, it took me to a black screen, seems a command page with no title and no ability to type down anything, though there was a cursor blinking.
This attempt I have made new partiotions, a root "/" , swap area and home "/home" and have chosen to install bootloader on its default value (my disk name indeed). And during installation I have faced with "GRUB installation failed" message that took me to this page to write it in forum.

I'd appreciate any help as I have few information around Linux. I'd ask you to provide me information about which partitions I need to make during installation and how much of space each (previously it was 8GB swap, 80GB root and the rest as home).

To be noted, I have had Win. 10 installed on drive C, and had two other drives as data which I want to be conserved, so I have tried all these by formatting drive C in partition stage of Ubuntu installation. That's because on windows I had disk problems which made me to install new OS.

Thanks for your help

ProblemType: Bug
DistroRelease: Ubuntu 16.04
Package: ubiquity 2.21.63.4
ProcVersionSignature: Ubuntu 4.10.0-28.32~16.04.2-generic 4.10.17
Uname: Linux 4.10.0-28-generic x86_64
ApportVersion: 2.20.1-0ubuntu2.10
Architecture: amd64
CasperVersion: 1.376.2
Date: Wed Jan 17 10:56:10 2018
InstallCmdLine: BOOT_IMAGE=/casper/vmlinuz.efi file=/cdrom/preseed/ubuntu.seed boot=casper only-ubiquity quiet splash ---
LiveMediaBuild: Ubuntu 16.04.3 LTS "Xenial Xerus" - Release amd64 (20170801)
ProcEnviron:
 PATH=(custom, no user)
 XDG_RUNTIME_DIR=<set>
 LANG=en_US.UTF-8
SourcePackage: grub-installer
UpgradeStatus: No upgrade log present (probably fresh install)

[Phillip Susi (psusi)]

Your disk is currently partitioned to boot in bios mode, but you booted the installer in EFI mode. A warning message prompted you that this could be a problem and recommended performing a bios mode install instead, but you chose not to. You either need to perform the bios mode install, or partition the disk using GPT and set up an EFI system partition to install in EFI mode. This will be done for you if you choose the "use entire disk" guided install option.