Adobe Light-room vs Photoshop

They are very different programs. Lightroom is an image management program. Essentially, LR is going to help you keep track of all of your images. In addition, LR has a powerful set of editing tools, but nowhere near the power that Photoshop has in terms of editing tools. On the other hand, as mentioned, Photoshop is arguably the most powerful image editor on the planet, but it doesn't offer anything like what LR does for image management. As example, in Photoshop you could open an image and create a layer of text saying anything you want. You can't do that in Lightroom. But in Lightroom, you can work with version sets of an image, say one version is B&W and the other is color but there is only one master image... you can't do that in Photoshop. In general, I would recommend starting with Lightroom (unless you are on a Mac and then I would suggest Aperture). If you find you want a more powerful editor, you could always look into Photoshop Elements. Elements will do most of what it's big brother will do (especially in terms of 8-bit photo image editing) for under $100.

Whatever your decision, I would join Lynda for a couple of months so that you can learn the applications. Either (or both) are going to have a learning curve.