What image formats to use for basic 2d animation?
That depends on what kind of animations you're planning. I would ask the artist to give you the project files (.psd if he is working in Photoshop, .ai if he is working with Illustrator) so that you are not limited to one final image (of course in that case, you would need said programs on your computer. Consider that if the artist uses CC and you're using CS6 or older versions, project files might not be compatible). If he refuses to send you the project files (which, in my experience, many graphic designers won't do), I would probably ask for high-res .png files (since they support alpha channels) if the artist's work is pixel-based. If the work is vector-based, ask for some vector format like .svg.