Beginner? Ubuntu (any flavor) is great in that they have a solid platform and generally everything just works. It's much closer to being a drop in replacement for commercial OS's, so if you are coming from Windows or OSX, I would suggest trying that first. It's based on Debian, so of course Debian would be a reasonable choice. Fedora works well and is easy(ish) to install as well, but overall Ubuntu has had the best app support.
Advanced? Try Qubes-os, that thing is pretty amazing. Definitely not for everyone, but it's an operating system that lets you run multiple OS's at the same time with no slowdown. It comes with Fedora/Debian/Whonix and it's quite easy to run Arch etc. at the same time.
Interested in the guts? My personal fave is Gentoo, they tend to have great docs and some very smart people work on Gentoo. It's the one you use when you really want to understand how Linux works. It's not a good idea for beginners. You install and compile everything from scratch. It's an older project though, and recompiling everything all the time can be painful. That being said, you WILL learn how Linux really works.
Cool Factor? Qubes-os ;) Of course the safe answer is any version of Raspbian on Raspberry Pi, because you can make real world changes to your environment.