You didn't do wrong in getting Elements -- it is actually a very good tool that you can do a whole lot with, including Raw processing -- it has a "stripped-down" version of Camera Raw that is included in CS4 (and shares the processing "engine" with Lightroom).
So, the differences: CS4 is the "Big Daddy" -- it has the top-of-the-line Raw processor, organizing tools, the top-of-the-line image editor, and great tools for automation and working with large numbers of files in batches and what-not.
Elements has many of the tools that CS has, but, like I said, the Raw processor is stripped down and it's not so good at things like automation and batches (I'd say no good, but I haven't used Elements since version 4 and I've heard that the newer versions have more capabilities. Many people happily use it, though, some because their volume doesn't require the advanced capabilities of CS, others because they have a good Raw processor that handles many if not most of their needs, including batch processing. Which brings us to...
Lightroom shares the state-of-the-art Raw processor that CS uses, but that's where the similarity stops. Lightroom was designed to be a workflow manager for photographers -- initially for Raw photographers especially, but it quickly embraced processing jpegs, psds and tiffs so that it can do a lot for any image. It has an integrated interface, rather than the typical image editor (such as Photoshop/Elements) where you have to hop from an organizer to a Raw editor to an image editor to endless dialogs to get work done. And, Lightroom has enough tools spanning so many basic needs that many of us do the majority of our work in Lightroom (and when I say the majority, I mean that opening Photoshop/Elements/whatever is a bit of a rarity). However, Lightroom does not have the special tools that Photoshop/Elements has for advanced image editing. So most of us have both.
Of course there are a variety of great tools out there -- in fact Canon's DPP has a lot going for it as far as learning Raw processing and doing most of what you need in that regard. But of the three you mentioned, for a Raw shooter I'd get a trial version of Lightroom and work with it with Elements as your "if needed" image editor and see how things fly.