If you can afford it, or somehow stumble across a *cough* free copy, get Photoshop, simply because it's easiest to find tutorials for it and you can do a lot with it, if you invest the time in learning how to use it. Otherwise, GIMP is a good image editing program that's fairly popular that's free.
For videos, start with Windows Movie Maker (free from Microsoft) if you're on Windows, and then, if you find it too limiting, look into a higher-end program like Adobe Premiere. You can do quite a lot with Movie Maker, so I'd highly suggest starting with that. Adobe Premiere is the high-end option there, but it's a bit overkill for camming videos, unless you're really serious about producing a lot of videos with high production values.