Linux is by far the most common free OS and is the only one discussed here. One example of another is BSD (Berkeley Software Development)
that Apple OS-X is based on (apparently more like unix rather than linux). BSD was developed at UC Berkeley with Federal research money and therefore
had to be made available to the tax paying public at no cost. Thus Apple's much lauded OS-X is based on a government funded program.

Linux is based on the UNIX operating system that was developed by Bell Laboratories for the communication business, in the halcyon days of
scientific research of the 1950's - 1970's. This OS was therefore developed by engineers for engineers (hence its obtuse syntax), and its continued 
use today is a testament to engineering insistence on practicality and stability rather than the marketing hype and ploys used by Microsoft and others.
Just think - if the US telephone system had been based on Windows you would rarely have been able to make an uninterrupted telephone call.  

There are many variants ("distributions") of Linux that are mostly incompatible with one another. These variants essentially differ by the way the
applications are "packaged", i.e. on how the application "sub-routines" are called from the OS. There are two major typed of Linux - Debian and Redhat, that
are essentially incompatible with each other. Examples of Debian based OSs are Ubuntu and Mint, and Fedora is the freeware version of Red Hat. Others include
Gentoo, Scientific Linux, and SuSE. I have dabbled with all of these and have found that Ubuntu and its sibling Mint are far superior for two essential reasons:
(1) User friendliness; 
(2) Many more applications. For example, I have found many more scientific applications in Ubuntu/Mint than in Scientific Linux (!). 

There are two  major drawbacks of Linux OSs
(1) Peripheral drivers (printers for example) are scarce. HP and Brother have the best support. I strongly recommend  Brother. In  particular
I have had excellent experience with the B/W laser AIO Brother MFC-L2700DW and the Color inkjet AIO Brother MFC-J825DW.
(2) Their "updated" versions are usually not backward compatible. I recommend Mint18 because these dependency omissions are mimimal.

NOTE: Windows8 and Windows10 appear to have taken steps to make use of alternative OSs difficult or impossible by defining their own
BIOS and therefore overiding GRUB2. A work around is apparently possible if the computer motherboard uses UEFI (or similar) rather BIOS - outside my bailiwick.

Multiple OSs can easily be installed on a single computer (for Windows <= Win7) but it is importan that Windows be installed first. The reason for this is that
Windows automatically erases all booting systems such as GRUB and installs its own. Dual booting with Windows 8 - 10 is much more problematic. However a solution
posted on the Web has got good feedback:
In terminal mode in Windows run  bcdedit /set {bootmgr} path \EFI\ubuntu\grubx64.efi. But Microsoft will probably find a work around sooner or later.
There are several options for trying out a Linux system:
(1)  Install as an application on Windows (up to Windows7).
(2)  Run from a CD (slow).
(3)  Install on a bootable USB stick.
(4)  Install on a HDD on a separate bootable partition (preferred but requires care).

Options (2) - (4):
(i) Go to the distribution site (for Mint it is 32bit:
                                                            64 bit:
(ii)  Download the 32-bit (i386) or 64-bit (AMD64) iso file from one of the sources ("mirrors") given on the page. The download will take a long time.
(iii) Burn the downloaded iso file to disk using the burning app of your choice. I use K3b on Mint.
(iv)  Before shutting down, insert the iso copied disk into the CD of your PC. Then restart.
(v)  Use the appropriate key to boot from the CD (depends on the motherboard, often Esc, Del, or F12). Correct key is displayed at the beginning screen of the reboot but sometimes
the time interval for the display is just a few seconds. Recently the installation CD automatically becomes accessible upon restarting without specifying the boot device.
(vi)  Follow the instructions for installation. For Mint and Ubuntu you will be presented with a Mint/Ubuntu desktop  with an "Install ..." icon on it. Double click on this for
installation BUT BE CAREFUL TO CHOOSE AN OPTION THAT DOES NOT WIPE OUT EVERYTHING ON YOUR PC! I always use the "something else" option and partition
 the HDD(s) manually. Heads Up: Sometimes the GRUB bootup program gets screwed up and you end up with an unbootable system, or your system does not recognize Windows.
IF you can get into one of your Debian Linux OS go into the Terminal mode and enter 'sudo update-grub'  in the command line (you will be asked for your password). For the handful
of times this problem has come up for me I have found that this command line entry usually fixes the problem. In the single instance where I could not get into LInux I inserted my
Windows CD for re-installation and went back to step (iv). Somehow I got into Linux this way (go figure!) and I could use the command line successfully. If your PC system did not
come up with a Windows disk but just an installation on your HDD and you did not make backup disks that sometimes come as an option then you are probably out of luck. In another
case the 'sudo update-grub' command did not correct the problem of Windows not appearing on the boot-up list of OSs and I had to re-install a Linux system to correct the GRUB loader.

 Dual Boot Sequence
  The order of bootup OSs can be changed within Linux using an user program that is contained in a LINUX repository generically termed ppa. To install
this program:
(1)  Enter the TERMINAL mode.
(2)  Enter (without quotation marks) "sudo add-apt-repository ppa:adabbas/1stppa"
(3) After entering your password enter "sudo apt-get update"
(4) Enter "apt-get install grub-customizer"
(5) Execute the Grub Customizer application
(6) Using the keyboard arrows move the OSs to the order you desire. I suggest you place all the backup OSs to the bottom of the list.


Ubuntu and Mint Linux
These two distributions are unusual (unique?) examples of mutual compatibility. Mint has two desktop options, MATE and Cinnamon, that must be downloaded and installed separately.
I much prefer MATE because I can place shortcut icons anywhere on the desktop that I choose, as opposed to what Cinnamon confines me to (that is similar to Ubuntu's Unity desktop).
The MATE desktop is similar to Windows 7 and precursors but with additional conveniences (such as choosing the size of desktop icons, easily moving launch icons along the task bar,
and tailoring the apperance and size of the task bar. Also, an  icon on the right side of the task bar indicates the status of updates - a check mark that indicates that there are no current
updates and an italic "i" that indicates that there are. You choose when you want update by clicking on the icon, not the OS.

The following information is distilled from my experiences with MINT18 and earlier, but much of it is probably appropriate for other distributions. I use Mint18, 
(1)  When installing Mint18 check the box asking if you want third party software to be installed - it is proprietary but free.
(2) One convenience that has not changed is the icon on the right side of the task bar that indicates the status of updates - a check mark that indicates that
there are no current updates and an italic "i" that indicates that there are. You choose when you want to update by clicking on the icon, not the OS.
(3) Installation of drivers: these are often found on the manufacturers' websites but usually in a zipped file (e.g. with a ".gz" filename ending). These can be a pain. There are two practical
options but before using them make sure the CUPS app is installed
(i)  Use the extraction app of the distribution you use.
(ii)  Use the chmod functionality in terminal mode. Consider a zipped driver  "Linux-Installer.gz" in some folder (e.g. Home/Download). To unzip this enter "sudo chmod Linux-Installer.gz".
where the file ID can be dragged from the folder icon directly into the terminal. This will produce an executable file in the folder that you will have been asked to select earlier.
(iii) Enter "sudo filename" where filename uncludes the folder (just drag).