From this, I assume that I don't need a resistor on any leg but the Red when powered from a 3.3v system.
Yes you do, see this page:-
http://www.thebox.myzen.co.uk/Tutorial/LEDs.html
Everything about this seems to be tailor made for my potential 8 LED project except of course that it would be limited because I need a total of 24 outs. So three of these???
Yes three chained together would be fine.
Do not put a capacitor on the latch pin, that is an error. Put in instead between +5V and ground close to each chip.