Evening Star,
Elements is a great application for touching-up pictures and actually doing some quite complex things with them. The "Transform" tool, for example, is a very powerful, yet easy-to-use device to change perspective.
The full version of Photoshop adds many more features suited to the pre-press market with many layers of colour control and more ways of creating artwork. If you are just cleaning up your photo scans, Elements should be enough.
Aperture is a different application from Photoshop. It is very much geared towards simpliflying the workflow and lightening the workload of the photographer. It can manipulate RAW photographs in real time, but deals with them in a different way from Photoshop. It has a lightbox feature, which aims to recreate the working environment of the professional photographer to make the workload more fluid. However, there are imaging controls within Aperture, but specific to photographers, particularly those working with RAW images.
Aperture also has powerful tools to make websites and web galleries of your images very easily, without needing to know html programming. Similarly, it can produce books in the same way as iPhoto, but you don't need to use Apple's templates; it is possible to design your own templates. Again, it's not hard and is geared towards getting the job done, rather than bogging you down in programming html or desktop publishing.