I'm incapable of being as concise as timl there... that's a very good, brief, yet helpful post.
You said you thought there were only a few types of Linux and found out that there are thousands... well, for the most part, THERE REALLY ARE only a few types. I'll get flamed for that perhaps, but seriously, E-V-E-R-Y-T-H-I-N-G came from Slackware, Debian, or Red Hat in some way or another, as evidenced by the GNU/Linux Timeline
. It's not been updated in a couple of years but it still shows my point very well. In fact, it all started with a base kernel written by Linux
Linus Torvalds of Finland, so really, there's only one "Linux" and everything else is a derivative.
Anyway, if you keep in mind the source distros you can basically guess how things will go down with respect to things like package management and system installation (not that you would know these things -- they come from experience). Take the time to install one system, and if it doesn't do what you need or want, try another, then another, and eventually the similarities become... well, numbing in a way. I've wanted to find a new distro for some time but lately they all seem the same to me, with the same desktop environments, the same window managers, the same buggy PDF reader set for default (with a perfectly functional one available for easy download). Debian based distributions will likely use one package manager, while Red Hat based ones use another... They'll either use SysV or they won't, they'll use polkit or they won't... Subtle and not-so subtle differences that I never cared about as an end-user of home equipment. Just make sure I've got a firewall (it's built-in) and I'm good.
As an I.T. professional, though, I kinda have to care about them for my work equipment to maintain security while also bringing ease of administration.
There's really no need to learn the "command syntax" for most purposes unless you want to become more familiar or perhaps more efficiently perform certain specific tasks (like changing system policy to allow all end users to manage their own WiFi connections). Recent distributions with graphical interfaces make most, if not all, day to day operations trivial. You'll probably be best served by a recent popular distro like OpenSuSE (what I'm using now), PCLinuxOS (what I have on my home machines), Fedora (what I have on my work desktop machine), Zorin (what I recommended to my father for its Windows-XP look and feel)...
That's a lot of suggestions and even then it's only the tip of the iceberg. Timl reminded me of Mint, which I've tried, and liked at first until either I updated or installed something and broke it all... I've also tried Sabayon, Vector, Arch, Mandriva... I've tried so many distros I can't even remember half of them. BUT, that's how I get a feel for things sometimes.
One of the more popular distributions is Ubuntu. It by default uses a GUI called Unity that resembles the touchscreen interfaces of Windows 8 and just about any smartphone. It has fairly easy setup and true to Linux form there are a million and one derivatives of it already, most with "untu" ending their names.
One of my favorite distros so far is PCLinuxOS. Its package management is quite similar to Debian, but with more recent software, and just about any software you'd want. I use it for web browsing, youtube (although slightly glitchy on my hardware), music... I've even authored a slideshow DVD with custom menus and backgrounds for a school function with it, as well as digital video editing, audio editing. Reads PDFs just fine (some distros default to glitchy readers but this one's fine). Day to day, it does well for me.
I'm using openSuSE on my work laptop to type this. So far, I'm loving it. It has its quirks, but that's what Google is for, and so far I've gotten just about all of them handled. The only thing left is to see if there's a way to enable some kind of palm-detect for the touchpad because my palms keep tapping it when I type, moving the text to wherever I happened to park my cursor last.
I think the best way to learn it is dive right in, ESPECIALLY if you have a spare [or virtual] machine you can install onto without worry of fouling anything up. Install a distro with all the options like desktop environments, and just USE them. See how they're alike, see how they're different. Most of the differences are subtle.
As to desktop environments:
LXDE is my environment of choice right now. Classic app menu look and feel with desktop icons, file management, etc.
XFCE is a close second. Can, but doesn't have to, have a desktop, and the look and feel is usually similar to Mac OS X.
IceWM is a very minimalist environment, with classic app menu look but very light on resources (read: it looks like Windows 95 would have if it existed in 1989)
Unity is the immersive-interactive touchy-feely that all the kiddies love. Not my thing but to each his own.
Cinnamon, Mate are basically imitations (visually) of classic GNOME, a more business-y app-menu-with-desktop that for want of better word "competes" with KDE.
GNOME is a kind of in-between of ... I dunno, Windows 8 and an iPhone?
KDE is probably one of the most popular non-Unity-flavored environments, and is very configurable with respect to look and feel, but like many others is a classic app-menu look with desktop icons.
Wow, I type too much. Hope this helps, and like timl said, ask all the questions you want. It's why we're here!