Lightroom and Photoshop are 2 very different things.
Lightroom is RAW processing and catalogue (and more now with LR4). You can make basic adjustments to particular set of parameters, such as WB, exposure, colours, levels, toning, sharpening, noise reduction, etc. You can make local adjustments as well now, but IMO, nowhere as advanced as Photoshop when it comes to pixel based adjustment.
Photoshop is purely a single image manipulation software (although you can get it with Bridge, which does a lot of what Lightroom does, to be fair). It's a lot more complex, but as a photographer, you will probably need only about 15% of its features. Very helpful when you know what to do. It's a very steep learning curve, and not easy on your wallet neither.
What you need will depend on how much photo editing you see you will be doing. If it's basic stuff like correcting exposure, removing a few dust spots, correcting red eye, playing with a bit of colour, convert to black and white, then Lightroom will do the job perfectly well. If you want to start going into finer details, or multi layer editing, then really Photoshop is the way to go. I have never used Elements, so cannot even comment.
However, if you decide to go down the Photoshop route, don't even bother trying CS6 on trial if you don't even know the difference between Lightroom and Photoshop. It will go straight over your head. Start to crawl before trying to compete for Team GB

For a beginner Photoshopper, I would say Photoshop 7 is powerful enough to learn. You can pick them up for peanuts on ebay (there's one going for £30 now). Fundamentally, not much as changed, although each release does get better and better, with added features. But it's like saying your first car must be the latest S class Merc, when all you need is a E reg Fiesta
Enjoy. It's amazingly useful and fun once you grasp the concept!