Color choice is completely subjective. Don't use greens. I hate greens (kidding . . . example in action.)

However, how you combine colors is not [accesskeys.org]. (see bottom and test any page . . . )

WCAG Guidelines:color [w3.org]

A crash course in color theory will give you real-world formulas for choosing complimentary, tertiary, triad, and other color schemes with discords and learn to assign dominance and submission in both shapes and colors.

Also there is a really nice (I believe it was done in flex) color scheme generator out on the web that I find helpful. Just do a search for it (sorry can't put the link up). There are a few more as well. But I will suggest that you read the WCAG Guidelines to color first. That way you kind of have an idea of what you are doing before you start.

White. Gray. Pale colors, and only if you must use color.

The above user is close to being correct. Neutrals and colors that will allow the emphasis of the site to be directed to the artwork and not your 'fancy' buttons, text boxes and obnoxious background patterns. [colorschemer.com...]
Color schemer is a nice program for generating color pallettes (triads, complimentary, pastels), but I hesitate to even recommend it to you because you are right to look to the example of museums. Warm greys, whites, black, solid colors or even cinder block (like my old art school used to prefer).
Again, this is subjective to what art you are hanging on the wall. If the painting is all blues and greys, but is making a statement about the color orange, you want to be sensitive to that and provide a background that will let the work 'speak'. (ie dont make a rusty orange background that will blow away the very thing the picture was all about - sublety and the relative hues of appartent orange in the absence of anything chromatic nearby.)
If you need real world examples:
[ecx.images-amazon.com...]
The 'Wow' seriers books all have subtle backgrounds because the are emphasizing the foreground and textural effects that photoshop can accomplish.

thanks!