Lots of advice here, mostly all over the place. Some I agree with, and some makes me crazy. So rather than comment on that here's my take, sotto voce.
If you are a photographer and understand the idea of a darkroom, Lightroom is the digital equivalent and will give you just about everything you would want to turn your digital negatives into photographs. The biggest bonus with Lightroom is that it's not just a great tool for post processing, it is also a complete catalog and workflow management system, allowing you to organize all your work, maintain and update metadata, and also publish your work directly to many online sites (Flickr, Facebook, 500px, etc.). The Develop module, as of LR5, is an enhanced version of Adobe Camera RAW, giving you tools that you do not get in the ACR that comes with Photoshop, like automated perspective correction. Even if you think you may one day want to get into Photoshop, knowing and having Lightroom on your computer will both ease that transition and allow you to better manage your workflow.
As for recommendations, I'm on the side that says, "Own your software". That said, given that you have no software now and LR will run you $105, going with Creative Cloud is almost a no brainer at $10/month. If you hate it you can get out in under 10 months and be ahead of the game (you won't). Plus you will immediately get access to full blown CS6, which you can ease into in any way you want. LR will always be available to buy down the road, and the promise is that they will be maintaining it as a standalone, so if you find after a year that you're not using the full complement of the CC suite then buy the next version of LR and drop the subscription.
But to start, download and use, use, use the 15-day trial of Lightroom. Find a getting started with LR5 tutorial and watch it. At the end of 15 days with it you'll see what it can do and make a personally informed decision. For me, there are more powerful image processing tools available, free and otherwise, but nothing as essential to my photography as Lightroom. I use so many things, but if I had to I could live without Photoshop, the Nik Collection and all the others, but not Lightroom.