Backing up files/folders you have saved to your computer can be done on your back up hard drive. That should be fairly easy. Some back up drives come with software, or you can download free backup software, or you can just copy and paste it if it's all in one place.
I've used FreeFileSync in the past and it's pretty easy to figure out. But my new (bought in the past year or two) back up drive came with its own software so I use that now.
Saving your favourites that are bookmarked is different. Typically you have a profile/account on whichever browser you're using, for example I use firefox and I can see there's a little icon near the top right that has my first initial, and if I click on that I can see details of my account. Chrome has something similar, I'm sure other browsers do too. If you don't already have one, you can create one.
So, if you have a profile/account and you know your password, then you can open a new computer, and put in your password on the browser over there, and there should be an option to import all of your bookmarks/favourites. I did this when I got a new laptop about 3 years ago and it was very smooth.
Hope that helps!



