Recommendation for Good Editing Software

While I'm not a beginner at photography, I have never done much in the way of post processing, other than removing those annoying dust specs from the image. I've started to hang out on this site more often in the past few months, and realized there's a whole new world out there in form of processing. I've decided I would like to delve into this, but I'm at a loss as to where to start. I've read a few reviews on Photoshop Elements, but didn't know if there is something better. In addition to standard editing, I think I would like to play around with HDR, stacking, and some time lapse stuff. Please advise what I'm going to need.