How do you go about backing up program settings. I want to reinstall
the OS without the added hassle of reconfiguring every application.

Such config files are usually stored in your "home" folder, in a hidden folder, that's name start's with a "."

For example; /home/james/.mozilla/firefox/ would be where on my PC Firefox stores it's settings for my user account. Hope I understand your question correctly.

Can you recommend a program that can save all my application settings so i can reinstall the OS.

I usually just manually copy the folders, rather than use a program per say.

Have a look at the following link: https://wiki.archlinux.org/index.php/Dotfiles

And also, if you have found something helpful, it would be nice to know, would you be able to mark anything you've found helpful?

The question is why do you want to reinstall your OS in the first place? Config files are scattered all over the file system, some are in your $HOME, some in /etc. You can easily backup whole operating system with rsync before reinstalling it so that you can always restore your previous settings and data. I would definitely do that.

The simplest way to achieve your goal is to have a separate /home partition. As mentioned above the user-centric modification are usually under /home in hidden files. I have used this on different releases and gone back to the previous release - all worked fine.
If you have manually updated things like the grub default file, you will have to re-apply those changes yourself. And of course you will have to re-install any packages you have selected - note that your settings for those will also be picked up ok.

I back up the following directory trees daily, with rsnapshot. The idea is to capture configuration files, but I also get log files, user emails, all web content, etc.
rsnapshot does incremental backups using rsync, so, with 7 daily 4 weekly and 1 monthly backup, they take up 50G on the backup server.
The production server shows 39.4G used, of which 38G is being backed up.

I agree that /home and /var (for web content) is mostly sufficient, but /etc contains many important files (doh!) and I use daemontools, so /service is important.

Check out rsnapshot.
One caveat: Out of the box, rsnapshot puts the backups in a hidden directory at /.snapshots...on my backup server, the / partition is 50G, so I nearly ran out of space before I reconfigured to backup to a directory under /home (which is 411G on that box)

I always reconfigure everything except email and browser. Otherwise, I forget how to do it. And old configuration files aren't always compatible to the new program versions. I also keep the old firewall script, and any custom programs.