Not a 74HC595, not enough drive current.
TPIC6C595 (100mA per output), TPIC6B595 (150mA), or TPIC6A505 (350mA) would likely be better choices for solenoids and a flow valve.
Attiny not much memory either (8K). Uno (32K), 1284P board (128K), or Mega (256K) likely a better choice.
An important fact is that the 1284P has twice the SRAM of the 2560 (16K vs 8K).
I've actually been growing to like the 1284P more than the 2560. I have not yet ever needed 256K of flash, but having lots of RAM has helped me several times.