How to select matching RGB and CMYK colors

Starting from scratch for a client, how do I select matching RGB and CMYK pairs?
Say we find a nice red colour in RGB for screen use, how do I then find the correct CMYK for print? And what assumptions do I have to make when doing this, if any?
Would it be the same for the other way around (choose CMYK first for print and then find the RGB equivalent)
Is it more sensible to start with a Pantone colour and then find the RGB and CMYK equivalents for that?
Many thanks
RobbieG
(I'm working with Ai, Ps and Id CS6)

Yes.  Better to start with Pantone reference books where you are viewing the color in a reflective environment.  As already mentioned, color on the monitor can be deceptive.  And, I think the others are basiclt saying that you should have everything calibrated and use color management policies in your apps.  There is a way to find CMYK equivalents using Photoshop's color palette.  Let's say you have an RGB Red as the foreground color in Photoshop.  If you double click on the swatch you will get Photoshop's color palette which lists the RGB percentages, CMYK percentages, LAB percentages, and HEX web color for that Red.  You can go further and select "Custom" and the Pasntone Spot color palette opens and gives you the closest Spot color value for that Red.  This however, depends on your color settings.  That's why I recommend you start with the Pantone swatch book and get the perecentages of CMYK from their formula guide which is set to industry standard color.

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