Types and colors of Oil Paints I should get?

Payne's Gray, its less harsh than straight black for shadows

For dot filters, a beginners set of mixed colors containing yellow, white, blue, red.

I often recommend Turpenoid, a refined turpentine.  It seems to be less harsh than mineral {white} spirit paint thinner.

Raw umber and lamp black are good ones as well as raw & burnt sienna.  I like to thin oils with Turpenoid.

Folks that do dot filters use a bunch of colors you wouldn't think go on camo equipment.  

I like windsor & Newton oils and have a couple Liquitex as well - they've lasted for years.

I did figures for a bit so my inventory may not be for all but I have:

Burnt & raw umber

Burnt & raw sienna

Titanium white

Lamp black

Naples yellow

Flesh tint

Cadmium red

Prussian blue

Burnt umber is always good for basic washes.