This is a long-overdue article since so many people ask about Photoshop versus Elements versus Lightroom. These are all different programs that serve their purposes and are worth their price and some when they are chosen for the right reasons. Since Adobe named them all Photoshop something, confusion is expected.
When looking for advice like this, people usually ask those around them. The trouble with that approach is that people recommend what they use without regards to the needs of the person asking. So, hopefully, this Photoshop Version Differences article can clear things up.