The BEST way to control white stair lights?

Here is someone a bit ahead of you LED stairs: the chips are talking | NovoKane.

What are your LED's power requirements? You mention MOSFET so I am thinking that they are higher then the shift register can handle. So you would not need a buffer unless you are locating the mosfet out near the LED. Speaking of MOSFETs... I think you really want a high power constant current driver, as high powered LEDs + resistors are not a good combination since the LED changes as it ages.

Cheers!
Andrew