For editing your photos, my advice tends to be to start out with Elements, and really learn it.
But the student discounts do make CS look attractive. The one issue is that getting the "CS6 Extended Package" leaves you "stuck" with that package for future upgrades. However, I'm not a student and so I don't know what the "real world effect" of this is. Hopefully some with experience can chime in!
Comparing Elements to the "standard" Photoshop CSx is worth doing. Elements has a ton of useful tools, and is likely all you will need in an "image editor". Where it "falls short" of the full-bore Photoshop, at least in my experience, is 1) Elements has a very trimmed-down Raw processor, which when I was using Elements meant a lot to me because I was preparing to get my first DSLR and to shoot Raw with it, and 2) Elements is (or at least was) limited in its ability to do things like automating processes and batch processing groups of shots. I'm not sure what has been upgraded over the years, but still "by nature" Elements will be "downsized" compared to the "standard" Photoshop, and since back in "the day" I was increasing my "volume" of photography, well, I decided to make the leap to the "standard" Photoshop (back then it was CS2).
And then there was Lightroom. I was happily going on with Photoshop CS2, but, like many of us, my growing volume of photos began to "pile up" on me, so that the issue of Digital Asset Management (DAM) became a real concern to me. Well, during that time reports were circulating about an upcoming Adobe product that would "package" DAM tools with the state-of-the-art Raw processor found in the Camera Raw processor used in PS CSx, not the "trimmed down" version found in Elements. All this stuff was to be integrated in a Raw Workflow Application, one that was being dedigned to be an "all-in-one" solution for most of what photographers wanted/needed to do.
This sounded great, I was "serious" about the DAM thing and also was seriously shooting Raw, so I grabbed the Lightroom Beta. It was "buggy", so I stuck with using CS2 as my "maing" tool, but over time, the Lightroom team did a lot of work to fix bugs. I had upgraded Photoshop to CS3, but after a couple Lightroom upgrades, good reports were coming out about the latest, plus they added support for jpegs, tiffs and psds, all good stuff, and so I jumped on board!
The thing I hope you "take away" from this is that dang DAM thing -- Lightroom takes organization "seriously"! There are plenty of options, you can pick and choose how you go about things, but right at the beginning, when you "Import" images into Lightroom, you want to choose your options wisely, otherwise you will likely regret it!
All that being said, my advice would be to first consider Elements compared to CS6, choose which will best meet your photo editing needs, commit to learning the program you choose. And, as you go, sure, "read up" on Lightroom, especially that DAM thing, so that if you do go with Lightroom, you will have a good combined "package" for DAM, a very capable Raw processor, and an image editor that will meet your more "extensive" editing needs!
As to Lightroom