Photoshop comes highly recommended and is the standard for many professionals. However, it's expensive. Adobe's "lightweight" alternative, Photoshop Elements, simply feels too barren, feature-wise, considering it is still paid software.
Paint.net is easier to learn but it doesn't have quite as many features, though all the essentials are there. It's great for beginners - especially if they're only familar with MS Paint, since the interface mimics it a lot. Free software, so why not give it a try?
GIMP is more of a free alternative to Photoshop. It can do a great many things and is highly customizable but be aware that it isn't necessarily the most user-friendly of the bunch.