Whether it's better to paint the background washes before or after painting the subject depends on what you are trying to achieve with the piece and how you want it to look.

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My personal preference is to mask my subject using Winsor & Newton's Colourless Art Masking Fluid, and then paint in the background wash. After the wash has dried, I remove the masking fluid and then paint in my subject.

The benefit to painting the background wash first is that you are less likely to mess up the foreground object. For instance, if you were to carefully paint in the subject first (say, a red rose) and then paint in the background, you would risk getting the background paint on the rose, which might mess it up. (Unless that is the look you are trying to achieve - an overlapping of paint - which is entirely possible.)

If you paint the subject first, you could try masking it (after it has thoroughly dried) with masking fluid and then painting the background, but then you risk the masking fluid peeling the paint off the subject as well.

There are times when I have worked on the background after painting in the subject, but it requires a steady hand to not get the paint on the object in the foreground.

There are, however, certain scenarios where you might want to paint the background wash before painting the subject. For instance, you could paint some light background washes and then paint your subject on top, with the color from the background wash showing through your subject. This can be used to create certain moods and effects.

For instance, if you painted a blue wash over your whole paper, and then painted a boat or a house or something on top of it, the blue would create a certain atmosphere in the artwork, perhaps suggesting dusk, rain, or mystery.

In general, if you want the background color to show through and become part of the subject, then paint the wash first. If you want to keep your background and your subject clearly and distinctly separate, then be sure to use masking fluid to mask your subject before painting your wash.