If you want to do pro-level work then you need a pro-level program, which would be Photoshop.
If not, Paint Shop Pro or GIMP, though I'd prefer the former.
Industrial Light and Magic used CinePaint (previously known as Film Gimp, which branched from the GIMP development tree in 1998) on 2003's
The Hulk. If ILM isn't professional, I don't really know who is.
Like I said, Photoshop versus GIMP is a long, drawn-out, and usually pointless argument. If you (or anyone else) wants to read about it ad nauseam, just google "Photoshop vs GIMP." There are plenty of arguments for one or the other. GIMP is great because it's free, it's constantly being tweaked and developed, it has a great online support community, and it doesn't cost anything. Determine what your needs, wants, and budget are and decide accordingly, but know that chances are for your uses there is no wrong answer. If I were you, I'd get GIMP running for free and play with it, and if for some reason you really need Photoshop later on, it's not like you wasted your money. That's what I did, and somehow I still use GIMP. . .
As to what programs do what, there are a few different types of programs and there are a few options for each type:
Photoshop and GIMP are high-level image editing tools with applications beyond photography. They are useful for everything from removing red-eye to making a big huge ugly watermark so no one steals your crappy pictures to make big profit (did that come out harsh?) or putting big glowing Gothic letters on top of a picture of your hideous custom Honda for all the world to see as your forum signature. They will not organize your photos. They simply give you tremendous horsepower to edit images of all types.
Aperture and Lightroom are tailored more towards photography. While I've never used Lightroom, Aperture is tailored towards professional photographers, designed to assist your workflow from camera upload to final output. Aperture has features like complete RAW support, stacking (to organize) and versions (multiple working copies), and others designed for the professional photographer. It will organize your photos and compress and store them in one large "vault," which the image editing programs will not do. The editing is tuned for photography, so you (may) not have the power to edit Goku into the driver's seat of your purple flame adorned Sentra for that sweet forum sig (not really sure about those heavier image editing capabilities, I know I never saw them). These programs are like professional versions of iPhoto or Picasa- the D2X to iPhoto's $85 point and shoot so to speak.
There are other programs that work as either add-ons to GIMP/Photoshop or stand-alones that allow you to perform specific tasks like reduce noise (Noise Ninja) or make HDRs (HDRshop).
To answer your question, a complete setup probably includes one organizing/workflow program like Aperture, one heavy-duty image editor for the heavy stuff like GIMP, and whatever stand-alones you need for your specific interests and style.
While it would be wonderful to start out with all of this software, a more realistic beginner setup could be iPhoto for basic editing and photo library organizing, and GIMP for serious editing. This is a completely free and very powerful software setup. You can always add other programs as you develop your skills and interests.