I would recommend the GIMP. It has features for both photo editing and animation. It is free, and it is available for all operating systems.
Other common ones are Adobe Photoshop and Paint Shop Pro (and Animation Shop for animated icons), but they are shareware, and very expensive too. You can download free trials, but they only last for 30 days.
Photoshop is more suitable for photo editing, and you can fix blemishes on photos, change the lighting, make colour photos into black-and-white.
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