Clemens:
24bit sound good, and "Internal Amplifier, Gain of 128" also, but 10mV x 128 is still only 1.28V...
That's still ~22bits of precision.
Connect SPEED to GND. (doesn't need an input pin)
Connect PDWN to 5V. (again doesn't need an input pin)
DRDY goes to MISO (pin 12)
SCLK goes to SCK (pin 13)
There is no "slave select" for this chip. That also means it won't play nicely if you try to put anything else on the hardware SPI bus.