When moving characters from one place to another location in animation, do you recommend moving the object center or the root bone? Moving the root bones seems to be doing the animation but the object center remains in the original zero location. Will it cause any problems?
Yeah, Jonathan is correct.
You will want to position your character in a logical starting position (object mode) but keep on the "animation" on the armature itself (pose mode).
Most of the time you won’t animate the "object", but you can think of it as a Master Root, or God Root as it is sometimes called.
What is a logical starting point?
Well that depends on the animation.
I see where some animators will put it at the start position, animate it I,e walking...then once done, use a Bezier curve to then have the character travel along the curve.... looking at maximo examples on youtube for examples...