I've worked with a version of Adobe Premier for video editing at school. It's similar to Sony Vegas which I have (ver 4) at home but I like Vegas a lot better. To do a cross fade with vegas, you don't need to hit a bunch of menu commands and then do it all over if you want to tweak the dissolve. Just drag one clip to overlap the other. It doesn't need to render to see the resulting effect. Much more flexible and easy to use, I even found Vegas to be easier and better than Final Cut Pro which I used at another university. Final Cut may have had more advanced features but I never got to find out as it was way too complicated just to open up the program and video files. I was surprised since I thought Mac was supposed to be more user friendly than Microsoft.
But I've heard a lot of great things about photoshop. I've never worked with it but I have used other photo editing programs before to crop, color correct and adjust brightness/ contrast.