I haven't posted to SD in years, but felt compelled to brush the cobwebs off and reply to your question...
1. This is a semi-religious question, so you are going to get a lot of vitriol in some of the responses; ignore it.
2. Gentoo is the "dive in the deep end, with weights tied to my feet and battle my way back to the surface" answer to your question. You build everything. You won't just learn the command line, you'll learn build tools, config scripts, environment vars, libraries, manual dependency management and more. I DO NOT think this is the right choice for you right now given how new you are to all of this. This will be the "death by a thousand paper cuts" experience that runs the risk of driving you crazy after 3 days of work and you still don't have a GUI running because of some esoteric error that you don't understand.
That said, if you insist that this is how you like to learn, go for it. The community/forums are very helpful and PACKED with information. If you do this, mentally prepare yourself for days and days of an unbootable machine. Reformatting and reinstalling over and over again. Getting a boot loader wrong, not installing Grub right, killing your install that was almost working perfectly because you changed a VGA boot option and now everything hangs... just prepare for these KINDS of things. Don't go in thinking "Awesome, I'll get this done in a day and have GNOME running" -- you won't, and if you do, something weird will break it out of no where and you won't have any idea what to do so you'll need to start over again.
I am not trying to scare you, just setting the expectation. If that sounds like heart-burn city, move onto my next suggestion.
3. Arch Linux -- You already mentioned this in your post and I just want to confirm that I believe THIS is the right choice for you. It is the perfect middle ground between Gentoo and something like Ubuntu -- you do get to know the ins and outs of the system, without the compiling/building/dependency pitfalls of Gentoo. This is an EXCELLENT place to start, get really familiar with everything and grow from (either down to Gentoo, or out of system management entirely into something like Ubuntu).
4. Ubuntu / Fedora -- Use these if you want a working computer, want to "try" Linux with a nice GUI and slowly become familiar with the underlying system through SOME GUI tools, mostly command line and have tons of support for your hardware. This is the "Mac"-esque experience you can get in Linux, in that you can live in the GUI all day if you want, but there is an underlying CLI/Unix world there under the surface if you want to mess with it.
5. Mint / SUSE / Kubuntu / Slackware / Whatever -- I have always seen these as different flavors of the same things listed above. I'd start with the primaries first and go from there.