You can select colors that give you the most flexibility by trying out the combinations on paper to see if they produce the secondary and tertiary colors you want. If they don't work, you can either change one of the primaries or you can change your intentions.
Here's an example:
Let's say you thought ultramarine blue and aureolin yellow looked promising, with burnt sienna as the red.
How about the reddest red? The ship on the right looks redder than the lifeboat pod on the ship to the left. Could you make that intense red with your palette? Even straight out of the tube burnt sienna will never be that red. Should you choose a different component? Well, that depends how you feel about the red you would get with burnt sienna. It definitely won't make pure red, but the rusty neutral it does make might be a perfectly good ship color. It's your decision.
The yellowest bit is another easy one. Will your choice of aureolin work for those wildflowers? Definitely.
Next, do the same for the secondary colors. What's the greenest thing in the scene? Can you make it using the components you chose? If so, great. If not, is the green you get when you mix your blue and yellow OK anyway? No? Why not?
The usual problem is that the combination makes too neutral a color. Secondary colors (green, orange and violet) are supposed to be a combination of two of the primaries. If your green is coming out too neutral, like an olive, somehow some red has sneaked into the mix. Aureolin is a greenish yellow, with just a hint of red - not enough to spoil the mixture. Ultramarine, however, is a reddish blue. Together the components may have too much red to make a pure green. Switching the blue for a more intense color (cobalt), or one that tends toward green (pthalo) will solve the problem at hand, but the new color still has to work for all the purples! Practice makes perfect enough.
The alternative is to simply select one red, one yellow and one blue, and let whatever combinations they make stand for green, orange and purple, like this fellow:
In the very neutral context, the subtle hues Wyeth made - like the blue-green of the gutter - look quite colorful enough.
Here are a couple more images. Select the 3 components of your palette according to whichever image you plan to interpret.