I am importing some clips from Premiere (Animation Codec MOV on Mac) and want to know if I should be setting the compositions to 8 bit or 16 bit. What's the difference? And if I worked in 8 and need to switch to 16 for better quality, do I need to start over?

if you gonna make heavy color corrections is better to go to 16 bits, otherwise 8 bits is fine (i´m assuming that your original footage is 8 bits, like DV or HDV or so)
You can switch back and forth 8 o 16 whenever you want.