Is there a way to tell photoshop to make the picked areas best fit a set of rgb values ?

The Kodak Q-13 is the familiar Color Separation Guide primarily used as a reference for color separation in preparation for print reproduction. The Guide, along with a gray scale, was helpful because a far better technology had not yet arrived. With the introduction of computers that reference card is inadequate. I suggest that, if color accuracy "on screen is as best as possible", you look into the lighting of the subject, your monitor color settings, and the X-Rite Color Checker Passport. The Passport manual in particular will be very helpful.

EDIT: One more reason to steer away from the Q-13 is that, although the grayscale is a photographic print, the Guide is ink-on-paper and over time the color shifts, particularly if the Guide is left out of its envelope. That instability translates to an unreliable reference. Some that I have seen in photographers' studios were downright grungy.

You can use the X-Rite color checker card to make custom color profiles in Camera Raw. I think that would be your best bet.

How to Create ICC Profiles Using the ColorChecker Passport with Adobe CS5

You can set the picket sample size to get a color closest to that area's color you do not  have to sample a single pixel.

You still get a single color value.  You should most likely add an empty layer on top. Then blend in some color you add to that added layer to adjust the composite image