Arduino SPI Clock Speed Configuration
You can set the SPI speed (and many other things!) using the Arduino SPI library without specifying any register values. You already did it with MSBFIRST. Like so:

  SPI.setDataMode(SPI_MODE3);
  SPI.setBitOrder(MSBFIRST);
  SPI.setClockDivider(SPI_CLOCK_DIV4); // 16/4 MHz
  SPI.begin(); 


Also, SPI.begin sets all the pin modes for you, so no need to do that.