I'm sorry, I didn't realize, that you wanted specific info on a package called "simple backup". I assume that's a linux mint addon package! I can't help you with that.
As for 'dd' and 'rsync' those are unix packages, what you learn there will apply to any distro you choose to use. Remaster and simple backup are Mint only I believe.
to backup my files and store them on a hard drive on another computer connected to our network in one or two steps
Backing up your files, again, you haven't defined "my files". That term backup can mean a lot of different things to different people.
One person "my files" would mean, just files he created such as .pdf, .doc, .txt, .html, etc.
Another person "my files" would mean all the above plus all the systems config files he's made changes to.
Yet another it would mean all the above two plus any special work he's done install propiorty drives to get his exotic hardware working, and any added on packages he's installed.
I personally just use hardware that plays nice with Linux, after using linux for some number of years, I've pruned my hardware, gutting any hardware that makes installations a problem. So for me a backup of my files is just /home/user directory only. Which contains all the configuration files for my email, webbrowser, desktop, and what ever else. It also contains my data, .pdf, .jpg, .html, and what ever else.
So rysnc works fine for my needs, it also works across all my distros, so as I don't have to relearn a method for each new distro I use. Like I said before I only use it for external HD backup. But it will work across a network, I've just never done it.
No one mentioned cron.
In your learning of rsync, they would have steered you toward cron, so that's why I didn't mention it. I don't use cron myself. But one can, it's a personal choice.
I asked if I had to do a full restore would I reinstall Daryna, install simple backup (or whatever I end up with) and then try to do a restore? I still don't know what to do. It was suggested that all I needed was the users home directory? Does that mean just copy that somewhere and then if I have to restore, copy it back over the newly created user's home directory?
There again, you haven't stated what exactly you want backed up and restored. I did a full install of Linux mint, doing a systems upgraded, jumping two versions newer at the same time. All I used was /home/user. And my system was up and running with all my desktop settings in less than 20 min. But that's me and my system, which doesn't require any configurations special to work properly.
Some of my programs reappeared, some didn't. Some settings were kept, some wasn't. It would be nice to know just what order I should do things if I had to restore to get my system back to the way it was without reinstalling a bunch of programs and then trying to reconfigure settings.
There is an old, saying "keep notes". I'm not much of a note keeper, but since using linux I've learned to keep note. In you statement "my programs", do you mean the programs you normally use? I use MC all the time in about 90 percent of the distros MC isn't there. So I have to install it. So now I just make a list of packages I need installed and after afresh install I run "apt-get install mc gftp sword" you can list as many packages in one apt-get as you wish, just put a space in between. (there is three in my example)
reconfigure settings= which settings? Yours? or System wide, (roots)?
All your settings are in /home/user, System wide are all over the place.
With rsync, you might have to be root, but you can instruct rsync to make a copy preserving the permissions, which will preserve your ownership. And you will be able to access the archive directly like a copy. it's not a specialt compressed archive file format.
Here's a link for using rsync over a network with cron. http://troy.jdmz.net/rsync/
Backups are a strange subject to get help on, because of the vast differences of oppion on what a backup is, and the vast differences of hardware involved. All we can do is sudjest and point. You have to tayor your backup to fit your needs. There has been hundreds of flame wars over this subject much the same as firewalls, over the years.