Many of the hosting providers now have tools on the cPanel for the site that can automate many of the aspects of moving a site for you.
Have you checked with your hosting provider? Many times their customer support, if they have a decent one, and that is becoming harder and harder to find, will assist you in moving the site. This is especially true if you are moving to a new hosting provider. Moving your site can be a part of the initial configuration that the provider provides.
Linux is a command line OS, and it is great to learn but unless you are really into learning the intricacies of an OS it can be a challenge. There is a lot to it. I would never discourage anyone from learning anything that they really want to learn but for the reason that you stated it may not be necessary.
Understanding the basics of Linux (Unix) is always good to know as a web site owner. There are some things that you can do for security on your site that are command line driven that can really help protect your files and directory structure that go beyond your typical .htaccess file.
There are ways to setup a Linux virtual box on your PC that can help you learn if that is the route you want to take. There are many different ways that it can be done, all you need to do is google .... "create a linux virtual machine"
That would be the simplest and safest way to get comfortable with the OS before jumping into the command line on your web server. Let's be honest, it is much better to make a mistake on a virtual machine where these is no impact, then on your web host where you could lose all your work.
One of the biggest things I stress to my students in class when working with Unix, there are no "Are you Sure?" message boxes when they issue a command. Once it is written and executed, it assumes you know what you are doing, and completes the command.
There is no "UNDO" in a command line OS. Unless of course you have a complete backup of the system prior to the command, which most of us fail to do, myself included.....
It has bitten me in the butt a few times.