[Beginner] Help in understanding what I need to power/test 4x4 RGB matrix

Hello,

My major goal is to build a 4x4x4 RGB LED Cube (and eventually, an 8x8x8). Obviously, that's a pretty big project, so I'm trying to work through things one piece at a time. Conceptually, I understand how it all works in terms of the signal processing/programming. What I'm not so confident about is the actual electronics of it. I'm going to be essentially following this tutorial, however I'm using these common anode RGB LEDs because I already had them on hand. Additionally, I wanted to use the 74HC595 8-bit shift registers because 1) I already had them, 2) the tutorial uses them) and 3) because they look like fun and I want to learn. I should note I'm using an old Arduino Duemilanove (should I upgrade? I think it's fine for this project).

As a way of testing things before I get too deep in the project, I wanted to take a single slice of 4x4 LEDs and see if I can play with it on the arduino - just to get a better understanding of how it works before becoming too confused with the full 4x4x4 cube.

I have the common anodes tied together in horizontal rows, while all the cathodes are tied together in vertical columns. This is a vertial "slice" of the cube. It looks like this:

What I'm not understanding is what other components I need to make this work with my Arduino for testing purposes. (By "testing" I mean not only checking that the LEDs work, but that I can also play around with the Shift Register - lighting each LED up one at a time, etc.) Having 4 layer anodes, and 4x3=12 column cathodes, that's a total of 16 pins, which I could play with using just 2 74HC595's, correct?

In the tutorial I linked earlier, he has each "layer" connected to a 2N2222 NPN transistor. However, his LEDs are common cathode - so my understanding is that I can't follow that tutorial to the letter. Would I need to use a PNP transistor instead? Where does the transistor go in a common anode set up like mine?

Would it be like:
5v > Anode
Cathode > resistor > transistor > GND

Or would it be like this:
5v > transitor > Anode
Cathode > resistor > GND

Or is it something else entirely? Any insight on this is greatly appreciated! Thank you!

For the actual building of the slices/layers, I followed this guide because I felt it was very consistent.

is there some schematic?

I apologize for not having my own specific-to-my-exact-situation schematic, as I'm still rather new to all this. I was trying to follow this schematic (but scaled down to only 16 RGB leds and two 74HC595s) - however I realize that he's using common cathodes instead of what I have (common anodes). So my question is basically how to modify this to make it work with common anode RGB leds? I'm not sure if it's possible to reconfigure it with a PNP transistor, or if I'm approaching the whole thing wrong entirely.

I'm not at the level where I can easily make my own schematics yet - I apologize for the inconvenience again.

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