iPhoto's probably best for your needs. Elements, as has been noted, is for photo editing. iPhoto, while it has plenty of editing features (just not good enough for serious amateurs and pros), excels at organizing, displaying, and sharing photos. Elements does not organize photos, and does not integrate with the Mac/iOS environment.
iPhoto ties into iCloud Photo Stream, iTunes syncing (iOS devices), Apple TV, mail, etc. - the whole Apple ecosystem approach.
iPhoto is free, and as has been noted, Elements can still be used for the sake of editing.