Lightroom is a photographers package. in that it allows you to catalogue, process and print you images.
The develop module is similar to the RAW processing option in Photoshop but has a much better user interface and in some cases additional options to the ACR module in Photoshop.
It can initially seem daunting but there are loads of tutorials and books on Lightroom , and from my experience is not difficult to learn.
For me 95% of my image work is done in Lightroom, with the odd excursion into Photoshop for those things that Lightroom cannot do. I suspect that if I didn't already own Photoshop I could probably get away with Lightroom and Elements.
Another advantage of Lightroom is it's now a lot cheaper than before and much less expensive than Photoshop.
Which package to have. Well if it was only one package then it would have to be Photoshop. However if you look at the price I'd opt for Lightroom and Elements.
Another plus for Lightroom, is structure. Photoshop is a very powerful program. However for some one starting from scratch it can be a bit daunting, and even overwhelming. How do I do this , How do I do that? Lightroom on the other hand has a much more obvious workflow. Plus there are numerous tutorials on the web that go through each module, explaining what each control does.
Here's a link to the Adobe web site that has a number of tutorials
http://tv.adobe.com/show/getting-started-with-adobe-photoshop-lightroom-4
You can download a 30 trail from the Adobe site for both Photoshop and Lightroom. Do the Lightroom one first I would suggest