Properly connecting Shift-Registers to microcontroller
You can always bit-bang the shift registers using general purpose I/Os. However, it may be more efficient (less processor overhead) to use the SPI interface. This assumes that the SPI interface is versatile enough to create the waveforms that you require.
The SPI interface on a typical MCU is fairly versatile. For example, many people drive WS2812 LED strips with an SPI interface.