The max7219 not only handles 64 LEDs by multiplexing, it handles also current limiting. To achieve all that using 595s you'd need two 595s, 8 current limiting resistors and a program to handle the multiplexing.
(MAX7219) and it's a much more complex chip to understand and use, especially for beginners (although various Arduino libraries make this easier than it would otherwise be).
Max7219 was designed for driving led displays, 7-segment, matrix or whatever.
It has built in series resistors which automatically adjust to the type of led (constant current drivers).
So, just to throw this out there I'm going to be using the MAX2719, I took a look at the breakout board I've got with an 8x8 matrix on it and realised I could just pull the matrix off it which exposed two lovely lines of 8 holes perfect for jumpering across to a breadboard for experimentation.
I'm actually going to try and drive 4 LEDs instead of one off each "port" so to speak.
The plan is to create a quarter of a circle with 4 x Red / Green LEDs (dual colour ones), so the ground will obviously go to the centre pins and then first 4 pins to the reds and 4 to the greens, allowing me to colour Red, Yellow and Green. Then each of these quarter circles will be duplicated 3 more times to create a full circle of LEDs (hence driving 4 LEDs per "port" [what is the correct term?]).
This whole shebang will then be duplicated a further 5 times for each of my targets (see blog thingy below).
Hopefully this kind of thing isn't going to draw too much current and pop the chip, the majority of the time there won't be much going on and very very rarely (if at all) will everything be lit. But hey, try it and see eh!
Put the LEDs in parallel? Not such a good idea, just give each LED its own position in the matrix.
If the targets are separated by any distance, you want to use one MAX per target, even if only half used.