The last few months I\'ve been using Emacs extensively as my main development environment and I\'ve now come to a point at which I\'d like to learn it\'s own Emacs Lisp to w
Start with Emacs Lisp (given that you seem to have already started customizing your emacs) - it seems to be more immediately useful for you.
Do keep in mind that there is quite a bit of difference between Emacs Lisp (there is a lot of buffer management stuff, especially in the code you're likely to see in the wild) and Common Lisp (more similar to a general purpose programming language), so which ever route you take, expect some amount of "wastage"
I recommend that you start with EmacsLisp, as it will be more immediately useful as already stated.
And as soon as you get a good grasp on the peculiarities of the language, you could start usingeieio.
To quote the emacswiki, it is An implementation of the CommonLisp object orientation standard (CLOS) in EmacsLisp.
Best of both worlds !