I am working on some of the concepts for a CG space animation and plan to have an orbital scene. I can only think of craft moving left to right on the screen, so the craft is going in a counterclockwise direction. Is this because of the right hand rule of physics, or are there examples of other orbital flight patterns. Any help would be a appreciated.
It doesn’t matter whether it’s clockwise or not. After all, what happens if you’re looking from the other side of the planet? 
If you’re going for realism, bear in mind that the relative size of a ship to the earth is microscopic, otherwise you can pretty much do what you like.
Incidentally, there are lots of different orbits. For example, some earth-scanning satellites have a zigzag pattern in order to cover the whole surface.