I use the ultimately pared-down primary palette: lemon yellow, magenta and cyan + white. This is the same color space as 4-color printing, so any color you can see in a 4-color print can be mixed with these.
Note that these are the primaries used in most schools in the EU. As a result, almost all suppliers of color from Europe have 'primary yellow,' 'primary red (magenta)' and 'primary blue' among their colors.
There is one caution: many of the EU suppliers add white to their primaries. This makes it hard to achieve a dark that's dark enough to serve as black.
There are certain pigments that behave well with each other (this is a key consideration if you want to avoid mud). Using these pigments results in almost-automatic color harmony:
Primary yellow: Hansa yellow (PY1 or PY3) -- Talens uses a mix of Bismuth Vanadate Yellow + Benzimidazolone Yellow 154 (PY184 + PY154)
Primary red (magenta) PV19 or PV19+PR122
Primary cyan, one of the phthalo blues, usually PB15:3
These avoid the cadmiums, especially the very orange-leaning cadmium red. Plus it avoids the very violet-leaning ultramarine blue. Despite the long tradition of use of both, they both contribute to many a muddy color mix.
Again, should you experiment with this, avoid tubes labeled "primary" that contain titanium or other white. The admixture of white helps school children (especially with the very powerful phthalo blue), but prevents a satisfactory "black enough" color.