Base Colors
Any model is still a model (see article), but in reality we are dealing with chemical elements and materials, and they do not always behave as we would like them to. Therefore, in order for triad paints to mix perfectly, artists usually keep two sets of basic paints: one warm and one cool.
Warm: Ultramarine, red like Scarlet, neutral yellow
Cool: Cobalt, a red like Alizarin Crimson, and lemon yellow.
From these three sets, I would reduce one of the blues. Both cobalt and ultramarine yield exemplary results. However, you will really need to buy the reds and yellows.
Of course, you can add as many paints as you want, but if you don't have the financial ability or space in your palette, this is the minimum set.
To this set, I would just add white and black, but more on that later.
Summary
As a first step, get yourself two sets of triads: warm and cool.