Thank you for your help and enlightenment, everyone.
Some final questions, though:
Is it possible (or easy enough) to add just some tweaks or pre-included software to a certain distribution? Or start from a certain distribution and add or remove the default software to suit my needs? I realize this may be possible using Gentoo or some of the more modular distributions you've mentioned, but is it possible to do a personal version of Linux Mint, with the programs I know I'll need?
And when it is said that a certain distribution is built off another what does that mean exactly? Linux Mint is built off Ubuntu, which is itself built off Debian, what does that mean in terms of things they have in common?