While the Lightroom + Photoshop CS4 combination suggested by a few posters is very powerful, indeed, it is likely to be overkill both price and featurewise for you unless you are a pro or an advanced amateur.

Photoshop Elements is seemingly rather simple but it has a surprising amount of power and it can usually fulfill most of the needs of non-pros with a much gentler learning curve and a fraction of the price of full PS.

I would characterize myself as an advanced hobbyist (DSLR with a lot of lenses, several thousand shots a month, almost exclusively RAW) and my own set-up is the following:

DxO Optics Pro 5.3 (for RAW processing) -- DxO gives much more fine-grained control over RAW processing than the RAW portion of Photoshop Elements. To me, it is the software I use by far the most (I typically correct exposure and color, and crop the image but do not do much more editing). The cost of DxO is around 100 euros. If you don't shoot a lot in RAW format, this is not a necessary (nor even a wise) investment.

Photoshop Elements 7.0 (about 100 euros again). Plenty of power and features for most non-pros. Very easy-to-use basic fixes, quite a bit of power for even quite advanced stuff. PSE has two components, Organizer and Editor. Organizer is keeping your shots in order and catalogued. In my experience Organizer is fine up to about 20.000 of so photos, above that it starts to creak a little. I go around this limitation by maintaining several separate catalogues instead of one huge catalogue.

Photomatix Pro 3 (another 100 euros) for HDR (high dynamic range) processing. This was probably not a good investment as I have found that I don't do a lot of HDR and there are some free packages for trying out HDR.

As some other posters have suggested, do go to Adobe site and download a trial to see which program meets your needs. There is a free trial available for DxO Optics, as well.

I have tried GIMP and gave up quickly as it seems to be rather powerful but the learning curve is quite steep. It is free, though.

Whatever software you decide to go with, I would suggest that you also get a good supporting book. I have Mark Galer's Adobe Photoshop Elements 7 Maximum Performance which I have found quite good (I only just got the book, though).

Hope this helps.

Cheers,
T.