best way to backup a PC useing windows 10 with external hard drive

Backing up is a huge topic, well beyond the capacity of a community forum. But I can provide an introduction here.

There are essentially two types of backup: a 'file and folder' backup and a disk image.

A file and folder backup is easy to understand. You copy files and folders from place 'A' to place 'B'. A disk image is more complicated.

A disk image is an exact copy of your entire hard drive, compressed into a single file. (To be technically correct, blank space on your hard drive is not copied.) This includes more than just the files and folders on your hard drive; it also includes the drive metadata. Metadata is information stored on a hard disk that describes the technical details of the disk. It's needed to restore the disk.

The most important thing you need to backup is your own data - your documents, music, pictures and videos. Software can always be re-installed, but your personal data is irreplaceable. Backing up your personal data is a 'file and folder' backup, and it's as easy as copying your Documents, Music, Pictures and Video folders to an external hard drive. Start now by doing that.

The only drawback to copying and pasting is that it gets tedious quickly. To make life easier, you want to get third-party backup software, which will make it easy to select files and folders for backing up and to schedule your backups so they happen automatically, every day. Your computer could be backing up while you sleep.

Windows 10 has File History, which makes backups of individual files and folders, but it's awkward to backup all your personal files in one shot. Third-party backup software is much better.

A disk image is great for backing up all your software. Imagine never needing to re-install Windows and your programs ever again. Instead, just restore a disk image and wham - you've instantly gone back in time to when your computer worked beautifully. Windows 10 has its own imaging utility, called System Image, but it really doesn't compare to third-party image software, which can do so much more and does it so conveniently.

There's your intro. For more details and plenty of hand holding instruction, just search the web. You'll find a wealth of information.

I use Macrium Reflect is a Free and Easy To Use Backup Utility to save a System Image backup, the modern way to reinstall in 20 minutes if Windows every becomes irreparable or the hard drive dies or needs changing. 

For file backup I prefer Windows 10's File History backup feature which will update each time you plug in the external, and allows not only backing up your selected files or folders, but also gives you access on the File Properties tab to older versions of the same file.

As you have the inferior Factory Install which most tech enthusiasts won't run in the first place, I'd consider doing the much better Clean Install Windows 10

which has no complaints or issues reported at all and compiles everything that works best.

Until then you can recoup significant performance by working through the Windows 10 Install Integrity Checklist  which will also clue you to much of what works best with Windows 10.