A leaking water pump will not cause white smoke out the exhaust, but can cause oil to get into the water or water into the oil or both.
It could be a head gasket blown to the water jacket. Be very careful with this. If water gets into the cylinder and you try to start it, you can easily snap a connecting rod or worse. The compression and leak down tests will let you know if there is a possible problem with the head gasket.
Overflowing coolant is also a sign of a possible head gasket blown to the water jacket.