The following colours are the primary palette used by the old master painters

They used these colours for a number of reasons:
They dry at the same speed,
Almost any colour can be mixed with them,
They are relatively easy to manufacture,
they are extremely long lasting, colour-fast
and have low toxicity and environmental impact during manufacture.
(Modern bright colours are pretty but can cause a lot of toxic waste)
The materials were readily available in the countryside (Umber / Ochre = iron mud)
Metal green was exceptionally rare and expensive.
Sap green was made from plant sap, like a dye, but turned brown after a few years.
After copper oxides were discovered it became possible to create vivid colours.

People in the printing industry will recognize the palette -
it is similar to Cyan, Magenta, Yellow and Black used to print modern magazines.
The above palette along with Titanium white ( don't use Lead White it is poisonous! )
will let you paint virtually any kind of portrait, landscape, or still life.

Limiting your palette also makes re-mixing colours easy.

Here are examples of paintings done with this palette:

A Muted Palette - Bouguereau's palette

Every colour was mixed with a neutral grey,
made from raw umber, pthalo blue and white.
The "black" was made with raw umber and pthalo blue.

A vibrant fleshy palette

White, Crimson and Ochre, with contrasting pthalo blue undertones

Seascape Palette

Pthalo blue and white, with a touch of yellow ochre

Renoir's Palette

Yellow ochre, white, raw umber and pthalo blue
strokes for the background, white,
crimson and raw umber for the foreground

Fiery Palette

Crimson Alizaron, Yellow Ochre, Raw Umber,
and Titanium white,
applied with a palette knife.