Backup Tool (Menu -> Administration -> Backup Tool, pre-installed in Linux Mint 18 and possibly earlier versions, lets you save a list of all installed packages. It's called Backup Software selection, with the corresponding Restore software selection. Save the file somewhere you can get at it after an install; Restore automatically restores the packages you had in the previous version.

For software that you have compiled and installed separately, I'd try setting up a Software directory in your Home directory and downloading and compiling new software. You have to set the Software directory contents to executable. Save this somewhere so you can simply recompile them after a total system reinstall if necessary.

Some more info regarding stuzog's answer above:

Mint's Backup Tool (mintbackup) is a GUI program that saves a list of installed packages by reading the entire list of installed packages on the system and then subtracting any automatically installed packages (found using aptitude ~M) and a list of packages that it maintains in /usr/share/linuxmint/mintbackup/software-selections.list, which consists of a list of packages that are installed when the operating system is installed (albeit only a subset as it appears for example to be desktop environment-agnostic).

The tool gives you the option to exclude further packages before saving the list.

When restoring the packages from a previously-saved list, Backup Tool essentially feeds the list into synaptic --set-selections-file.

As mentioned previously though, it would be advisable to use this only if you're restoring to a machine running the same version of Mint with the same desktop environment as the one you backed up.