This disaster tends to come about when a broken package (typically one with dependencies that cannot be installed due to their not existing or the user having set up a hold on a specific package version) is present or when the user has installed conflicting dependencies from a PPA. The -f flag tells apt-get to find any solution it can to remove all breakage from the system. In this case the 'solution' was to remove almost every package, so you must have had a really low level conflict somewhere. It looks at what dependency appears to not be installable and either installs or removes packages until it can install that dependency or until all packages that conflict are gone. I once had every piece of GUI software right down to X removed because of an improperly packaged version of Libreoffice.

You can see from this image that a bad wine package from a PPA could indeed kill the whole system:

If libc6 were to be replaced via a PPA with another version that would indeed cause APT to remove the whole system. Just about everything winds up depending on libc6 in the end, including the kernel I think. I'm not saying for sure this was it, just using this as an example to show how dependencies are interconnected.

You can use the LiveUSB to copy your files over before reinstalling or just reinstall with the advanced partitioning settings. I recommend just using the advanced settings to reinstall because it saves you copying any files off the disk, so long as you've not stored anything outside of /home and /srv.

You need to make sure that your ext4 filesystem is set to mount to '/' and that the box under 'Format' is not checked like it is in this image:

Anything not stored in /srv or /home will be DELETED.

If you wish to use the same username you should move or rename your home folder before reinstalling so it can be recreated with fresh configs from /etc/skel. You can then copy configuration files and data from where you moved it to their proper places after the reinstall. This is necessary as some programs (Firefox for example) will not pick up the config files from your old install automatically even if they're already in the home folder the first time you log in. Some programs need to be run first, quit, and then have their configuration files copied over.

I'm pretty sure for evolution you can just copy the .evolution file from your old home to the new one and have it work normally. You may need to run evolution once and close it before copying over like I mentioned above.

As per your comment on how to properly solve this issue, the manual for apt-get (the section about -f) suggests using dpkg --remove $PACKAGE to remove the package causing the problem manually. This should allow apt to run again as the package trying to pull in non-existent or un-installable dependency will be gone.

The problem that killed your machine is a fluke, it simply should not ever happen on a stable release of Ubuntu. The repository system is organized to prevent this from happening, but the addition of random PPA X throws a wrench into what is otherwise a perfect system. I suggest you examine closely the contents of your added PPAs and which software packages are installed (and upgraded to) from them. Several PPAs will upgrade important system packages in order to make the software they contain work. This is great until the newer dependency from the PPA conflicts with the older one in the repo. At this point APT will always install the newest one, and boom, your system will not upgrade any packages because the Ubuntu repo software is still in need of the older library version, which is not going to be installed.

The best of luck to you. Please comment if you have questions or if I can improve this answer.