In order to setup your PC in the way you described before, you can do a Manual Partition when you are installing ElementaryOS.
Since I don't know the level of experience you (or the person reading this question) have, I'm going to do a very detailed tutorial so it is clear enough almost for everyone.
I recommend you to firstly check this, basically there'...
Even if it works on the desktop, I would check the MD5 checksum from the elementary.io site after downloading the ISO and then re-create the USB (Balena Etcher should do the trick if you're creating from Windows or Linux).
Based on my experience doing the same with Ubuntu16.04 and Loki - If you keep the home partition it will be better to use the same username and password during installation - the password later can be changed safely but the username has to be kept. But doing like this probably some of the problems will be transfered into elementary OS also, because it is ...
It turned out that I found a self contained boot disk utility (maybe on the android x86 web site) that would just launch, then give you a menu option to boot the computer using the usb drive. That worked. here is one such utility:
Of course you can do it easily !
First of all, you need to create new partitions for eOS Distro (including his own swap if you have one for Mint (if both use the same swap, it's could have effect if you hibernate one and you boot the other one).
When you install eOS, or every linux distribution, by default an installation of grub is part of the linux distro ...
what do you mean by that exactly? Is elementary invisible in your BIOS? What happens if you select the partition that you installed it on?
If it just stays that way check if you have FastBoot enabled and Legacy Boot disabled. However I would require more detailed information for further assistance.
Remove refit(mac hd/efi) if it was installed.
Enter live usb with linux on it using refind bootloader, when grub appear press “e” and type “nomodeset” after “splash” then f10.
Install linux alongside mac os, (or else using only “/“ and swap if you want)
After installation refind will be replaced by grub2.
In grub choose ...
I know that with at least the elementaryOS 5.0 "Juno" install media you are able to create custom partition tables.
Proceed through the installation wizard, and when you get to the "Installation Type" screen, select "Something else."
From here you can add/remove/change partitions.
If you're using a different version or are used to using other tools, you ...
Can you please try hitting the 'e' key in the grub boot menu (text mode), and adding 'nomodeset=1' to the end of the line that starts with 'linux'. Then hit F10 to continue booting.
You should see something like:
(Googled image, not the exact line), Basically that's where I'm asking you to add the 'nomodeset=1' value at the end.