Hi William, glad to hear you're going to give it another shot. Take your time, and remember that you may encounter several difficulties along the way. Linux Mint may or may not be the best choice for your laptop, but if you like it then by all means pursue it as your first choice. Tell us more about your system before you begin, if you will. Such as:
1. Does it currently have Windows 8 or Windows 10 running?
2. If so, do you want to dual-boot and keep Windows? Or do you want to erase Windows and go Linux only?
3. Before trying to install Linux, have you tried first to boot up a "live" version on USB or DVD?
One of the "tricky" things that Windows 8 and 10 does is that it may not truly shut down when you tell it to... instead it "hibernates" so that it comes to life faster when you think you are booting it up. Being in a Windows hibernation state is not a good place to begin to install Linux, and booting on a live USB or DVD may give you a clue if this is happening. If you think this is happening with you... don't tell Windows to "shut down"... tell it to "restart" instead. A Windows "restart" bypasses the hibernation process.
But it still may not boot right away. Sometimes you have to get into the "UEFI" settings (what we used to call BIOS or CMOS settings). Anyway, more about that later. Let's see where you're at right now and try to figure out how to get you into Linux!
Cheers!