The 77311-127-16LF: The 0.260" (6.60mm) mating pin length gives enough engagement depth for most industry-standard female connectors without bottoming out. For higher current, you'd need to parallel multiple pins or move to a larger contact. The tin-plated posts (78.7µin) are fine for soldering; just don't use them as the contact surface in a corrosive environment.
If you need a second source, look for other 0.100" pitch, 16-position, single-row unshrouded headers with similar mating pin length — but verify the contact finish and current rating match your application.
Through-hole termination with a 0.105" (2.67mm) post length — fits standard 1.6mm PCBs with enough tail for a good solder fillet. The 0.465" (11.81mm) overall contact length includes both the mating pin and the post, so the board-to-board stack height is set by the receptacle's mating depth.