I have been tweaking this basic palette for a while. Trying to get the essential colors I would have my students get that would give them a wide range of colors with out busting their wallet.
So I have come up with a six colors that will give you all that you would need and a final 7th color that gives you some more bright mixing.
The Basic 6 colors are the following. I buy Daniel Smith colors for their intensity and richness (and they are a local company)
Hansa Yellow Medium
Transparent Pyroll Orange
7th optional Manganese Blue
Here are how the triads work and you can see what you get when you mix the paints.