Choosing what colours to include in your oil paint palette is individual to every artist, and depends on their style and their subject matter, but this post is just a brief look at some of the choices that are out there.
If you are good at mixing colours and want to travel light, then you can actually get away with around four or five colours. Yes hard to believe, but that is all you need if you have the skills to mix the colours correctly. Of course adding five or ten more adds to the expense of getting started but can make painting much easier, avoiding the task of trying to get that shade you want but can't quite figure it out.
The above photo shows four colours -- a very basic set, titanium white, French ultramarine, cadmium yellow and cadmium red. From these four, travelling light, you can mix all the shades necessary for to paint any skin tone, and paint portraits.
The photo next, shows pretty much all the colours most people will ever need, if they are reasonably good at mixing colours. They are as follows: Titanium white, Yellow Ochre Pale Hue, Yellow Ochre, Cadmium Yellow, Raw Sienna, Cadmium Orange, Cadmium Red, Permanent Rose, Permanent Magenta, Permanent Mauve, French Ultramarine, Cobalt Blue, Cerulean Blue, Viridian, Venetian Red, Raw Umber and Burnt Sienna.
And a few additional colours that sometimes I use to save time.... Cadmium Yellow Pale Hue (which is a lemon yellow), Naples yellow (a nice yellow for dusty desert scenes), Manganese Blue, Prussian Blue, Indigo, Oxide of Chromium ( a useful natural green), Indian Red (useful for skin tone when combined with white), Burnt Umber, and Paynes Grey.
Although some people like to include black, I have not included it here as I rarely need such a dark colour, and many nicer dark almost blacks can be mixed using other colours.
Anyway these are my suggested colour range if you are starting out, and can't decide what colours to buy. You can buy a few ( four), seventeen or all twenty-six if you feel like splashing out, but maybe best to start with just a few until you see how much you like painting....