The 74HC595 is not suitable for driving LEDs, it can only sink 6mA.
I repeat
STP16CP05 £1.51
TLC5916 £0.83 DIP package
TLC5926 out of stock but £1.04
from uk.farnell.com (don't know about P&P though)
and you don't need resistors, what's not to like?
Rob