How do you choose whether to use a TVS, clamp the signal, or both?
More often than not, I use both. You can get steering diodes and a TVS in the same package (PRTR5V0U2X). Depending on the nature of the signal, a series resistor or ferrite bead, and shunt cap can be beneficial. 

Forget that the IC in question has internal clamping diodes. Those are intended to protect the IC from accidents before it's soldered to a PCB. If you really want to use them as part of your protection scheme, definitely limit the current through them. A maximum clamp current may not be specified, and if that's the case, best to consult an applications engineer.