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What is the best program for 3D animation in which you can import files from SolidWorks and use it for animation ?
Depends on what level of animation you need. If simple and nothing too crazy needed, then Keyshot or Bunkshot.
If you want some of the best controls for animation, rendering, and modeling then Modo hands down. Depending on how you'd like to control the model then I'd recommend the "CAD Loader" as a plug in.
I would recommend using Blender for animations. As it is very cheap (free) and it does a very good job. But be ware any program that does a good job at animation has a steep learning curve. www.blender.org check it out. You can import OBJ and or stl files into Blender from SolidWorks. There is a free OBJ exporter that works inside of SolidWorks.