My Color Palette
I prefer the Golden brand of professional quality paints, because they are made in the US and have excellent color strength and lightfastness. There are over 100 colors available, but these are the ones I use myself. Notice that these paint swatches show the transparency of the paint in addition to the color. You can also visit my article about choosing paints to learn more.
Blues
Ultramarine Blue is a good color for skies. It's fairly opaque and can be warmed up with Pthalo Blue. Pthalo Blue can be difficult to use at first because of the high color strength, but once you get used to it and learn how to thin it down, it is quite nice for water. Smalt hue is very transparent and is surprisingly versatile. I use it often for shadows on faces.
Greens
The names of paint colors vary between brands and types of paint, but the base pigments are the same. All professional quality paints list the base pigments they use, so if you migrate brands you know what you're working with. Sap Green is one of Golden's historical colors, a synthetic version of a paint originally made from the sap of Buckthorn berries. I like it for painting leaves because it has a nice natural hue. Green Gold and Pthalo Green are very versatile transparent greens, but they both need a lot of mixing with other colors to produce realistic plant shades.
Yellows and Oranges
I originally just used Primary Yellow and Yellow Ochre, but they are both fairly opaque and tend to look chalky when thinned out in glazes. I added the Nickel Azo Yellow for tinting other mixes and bringing in transparent warm layers, when I want the underlayer to show through without being lightened.
Reds and Browns
Burnt Umber is a very versatile color, but I find it tends to range a lot in lightness when you go between brands, and it's very opaque. When torn between choosing two shades for your palette, I usually recommend choosing the more transparent shade, since you can always mix in some Titanium White or Carbon Black if you want opaque effects. I'm always on the hunt for a more transparent brown.
Pinks and Purples
I use Quinacridone Magenta and Dioxazine Purple in every portrait I paint. Violet Oxide is much more opaque and not as versatile, but it's a wonderful color for painting chocolate labs, so I use it pretty often.
Blacks and Whites
My favorite discovery when trying new colors was Zinc White. The transparency allows you to lighten areas with a lot of control, which is very useful when making adjustments in portraits or adding shine on tricky subjects like eyes.