My path was:
Caldera OpenLinux 1.1 - 1 year
Mandrake - 1 year
RedHat - 2 years
LFS - 2 years
Gentoo - 8 years and counting
With some HP-UX, IRIX, and debian sprinkled in on some non-x86 arches.
If your end goal is to be a master of Linux/unix in general:
I highly recommend doing LFS at least once. It strips away all the helpers (which sometimes complicate things), and forces you to know for each package how it natively behaves, their own config files, locations, etc. You learn what happens from boot on up to the login prompt. You learn what all the pieces are, what they do, etc.
I also highly recommend trying Gentoo at least once--at least until you learn how portage keywords and package use flags work so you can honestly compare to rpm/apt in other distros. Gentoo is a happy compromise--a step back from LFS in that it normalizes most of the configuration locations and services control, and adds full package management, but all while still allowing you to take finer-grained control selectively as you want/need. (Personally, I prefer gentoo's way of configuring services to the other main distros--it feels more flexible and less "in-my-way"ish, especially for disk layout and network configuration.)
From there, you can learn any distro you want/need. (But I'd guess that most people that give gentoo an honest try wind up sticking with it since it has fewer cons and more pros than most of the other canned distros. BTW, it does support binary packages--many do not know this.)
If your end goal is not administrative prowess, but simply to use it as a desktop:
You probably should stick to a well-supported end-user-focused distro such as ubuntu, fedora/redhat, suse. You may not get bleeding edge, but you won't bleed--and many help topics on the web cater to these main distros. IMO, for such an end goal it really doesn't matter which distro you use first--they will all have some shortcoming that will require some googling to figure out--no distro of any OS has all the kinks worked out.