Commercial printers have process inks ready to go off the shelf, and at the same time, the separations are designed to optimize the performance of the inks. So in the printing industry, everything is hunky-dory except for the one little thing, that the colors are not intended to be, and are not, permanent.
By contrast, in tricolor or four-color gum printing, we have to blaze our own trail to a large extent. While commercial printers just order up lots of "magenta" or "cyan" ink, we are faced with choosing from various red, yellow, and blue pigments, few of which are precisely the hue of process inks, and some of those few not being lightfast. This presents both a constraint and a freedom. Few gum printers are interested in matching precisely the color balance of a commercial print job; instead we enjoy the freedom and flexibility of "interpretive" color balance. I do not provide here a recipe for exactly reproducing an "accurate" color balance; in fact I don't provide any recipes at all, just some things to think about when choosing pigments.
There are basically four things to consider in choosing pigments for tricolor: (1) the hue of the color, where it fits on the color wheel, (2) the strength of the pigment, whether it can hold its own with the other two pigments, (3) how well the pigment mixes with the other pigments you've chosen to produce intermediate colors and/or the neutrals that can result when three pigments mix together, and (4) the transparency or opacity of the color. I'll discuss each of these considerations in the context of describing individual pigments.
Though the cyan layer is usually the last one I put down, (this is not a hard and fast rule; other gum printers print the cyan first to make it easier to register subsequent printings) I'll start with it here, because blue is the easiest. There are only a few blue pigments, and at least half of those aren't very useful for tricolor. While there are dozens and dozens of blue paints with dozens of different names, essentially all of these paints are made from six pigments: pthalo (PB15); Ultramarine, (PB29); Prussian (PB 27); Cerulean (PB 35); Indanthrone (PB 60); and Cobalt (PB 28).
The most commonly used cyan blue for tricolor is pthalo blue (PB 15 and variations). It is transparent, lightfast, gorgeous, intense. It's really the only choice for brilliant, jewel-like color mixes. It is a very intense color, so a little goes a long way. For some reason this is the blue that is most often given some other name for marketing purposes. If you've got something called "Winsor blue" or "Intense blue" or "Monestial blue" or "Hortensia blue" or "Hoggar blue" or "Delft Blue" or "Helio blue" or "Joe's blue," PB15 by any other name is still pthalo blue.
I personally use ultramarine (PB 29) a lot for tricolor. To my eye, it makes more natural visual color blends (especially natural greens in landscapes) with the yellow (PY110) and the red (PR 175) that I prefer for tricolor work, than does pthalo. The remarkable thing about Ultramarine is that almost every Ultramarine paint actually has the word "ultramarine" in its name, and conversely, just about every paint that's named Ultramarine actually has PB 29 in it, except for "ultramarine violet" which is PV 15.