bounding volume hierarchy/space partition

I have an object which is converted into triangular mesh. I have found
the AABB of the entire object So I would like to know what bounding
volume hierarchy/ space partition methods are possible. I would also
like to know if it would have been easier with a bounding sphere ?
What are the BV hierarchy/space partition methods in case of boundary
sphere ? I looked up BSP trees but I could not understand how they
choose the splitting planes. I came across codes for BSP in graphics
gems.