cascading shift registers 595 vs 594
If you don't need the /OE (tri-state) functionality of the HC595, the HC594 is almost equivalent, except for the /RCLR input (which the HC594 has and the HC595 does not have). Pinouts, except for the /OE and /RCLR pins mentioned, are nearly the same.



The setup you descibe would work for 3 cascaded 594s with individual RCLKs. As you have to shift in 24 new bits whenever 1 output changes anyway, you could ask yourself if you need 3 separate RCLKs (one might do).

The same goes for /RCLR on the HC594. A parallel reset is very handy if you can spare an I/O pin on the Arduino, but you accomplish the same by shifting in 24 zeroes on startup (which you would have to do if you had a HC595 anyway).