The 74AC299 is better for its current sink/source capability. The 74HC595 was designed to interface with other logic chips, not for driving LEDs.
24mA will be plenty. Most LEDs have limits of continuous On current approaching 30mA. Don't plan on running them that high.
If you get some 20mA, 5,000mcd LEDs from dipmicro.com for 5-6 cents, or from superbrightleds.com, they will amazingly bright at 20mA.
I just just used some of the reds, 2 in series with 100ohm resistor, and 2 blues in parallel with single 200 ohm resistor, they are bright.
If you are buying 20mcd LEDs, those will not be too bright at all.
I have 20 74ac299s on the way from newark.
download this datasheethttp://www.national.com/ds/54/54F299.pdf#page=1
I think it makes it a lot clearer what the connections are.
The part can be parallel loaded (vs just shifting in from 1 pin), and the bits can be shifted left to right, or right to left. So more of a universal part, can be used as a shift-in or as a shift-out register.
I will do some reading and check back in tomorrow. Have a pounding hedache tonight for some reason.