I am creating my logo in Illustrator (ready to place in InDesign as part of a DVD sleeve.) and I'm wondering if I should be choosing 'Spot Color' or 'Process Color' for my whites. (For the other settings I have chosen 'CMYK C=0 M=0 Y=0 K=0'.)
White is absence of color in most printing techniques.
If you use a spot color for your white and use a standard offset printing, it will count as an extra plate and you will need to modify or pay to have the logo modified to ignore that extra separation anyway.
You can use a white spot color when you plan to use your logo on t-shirts or plastic for example, but rarely on paper (offset.) On offset and standard printing, you can simply use a normal C0-M0-Y0-K0 or "divide/clean-up" the logo to remove the white parts by using the pathfinder tool!
Some links related to your question:
In a practical case in this situation, it is the same. Yo can leave a CMYK at 0 values, "white" or inclusive rgb white.
But there are some times when there is a diference. For example printing dark T-shirts. You actually need a white ink to be printed there. But sometimes you can define a very light gray spot color so other people know there is sonething there, and replace it with actual white ink.
You can consider, instead of putting a "white" part of a logo, for example the dots on a domino's pizza, and making a "real hole" on the blue square. This way there is no "white" on your logo.