separating your ammo and reloading data form the installed software is a very smart move. Normally there is no problem to re-install software. The real value is in your data, because your data files are unique.
I use three external disk drives in turn. So I have three copies of the data: todays backup, and two previous days.
What Backup software you use, is mostly a matter of personal preference. I use the program called robocopy that is a part of modern Windows versions. It creates a snapshot of a given directory on the external disk by only copying new or changed files and deleting files that were deleted in the current directory. Having more than one external disks limits the loss if one of your external disks fails. Also you can recover files deleted by mistake, as long as you detect your error in time.
The important things are:
a) Use separate directories to hold your data on your computer. Never mix programs and data in one directory. This limits the backup to a manageable size
b) Do not get lazy. If on a given day you downloaded new files or do any change to your own files, take the time and do the backup.
c) You cannot cover any possible disaster/criminal intent/error. But the typical data losses can be avoided.
External disk drives, connected via USB, have the advantage of being very fast, and compare well to CDs in reliability. Typically, my robocopy backup runs in less than a minute.
As I wrote in an earlier post: I work in a data processing center, and on average we have one disk failure on every working day. These are professional quality disks, not the end user stuff you find in ordinary PCs. Sooner or later it will happen to all of us. It already happened once to me on a Sony notebook. Sony replaced the disk, and I was really happy to have my backups.
P.S.: Mel is in my view neither paranoid, nor going overboard. I see it as common sense.
My external drives are not connected to the computer, except during backup.