Digital Painting

The most established applications for digital painting are Adobe Photoshop and Corel Painter.
If you are on a budget, give Mischief a try.
Two currently free alternatives to Photoshop that have made great strides are Krita and Affinity. The latter is Mac only.

Image Management and Post Production

The most powerful solution for working with photographs and digital images as well as keeping your files organized, is Adobe Lightroom. The key concept here is non-destructive editing, meaning your edits to an image are saved separate from the original files, which are left untouched.
Free and very fast alternatives are Picasa and XnView, the latter has powerful batch-processing and batch-renaming features.