Painting vs Painting and Primer
I rarely use primer on previously-painted walls unless the existing finish is suspect with regard to bonding. It's a disaster to have paint come loose due to incompatibility. 

The right primer color when doing dramatic color change is usually whatever gets you close to your final color. You want whatever underlies your topcoat to have minimal effect on the color you selected. That said, sometimes a base coat can affect the topcoat in desirable ways, such as making the color deeper or more rich. That usually applies to bold colors, though, and gray (or custom-tinted) primer is often appropriate. 

You ask about changing approaches mid-stream. That is a potential concern, but you'll have to try it and see. If the primer approximates what the first coat of paint did, it may not be noticeable. 

When painting white over white primer, it's usually not as difficult as you might think to see what you're doing. Wet paint has a gloss, dry paint usually has more sheen than primer, and the color is rarely that close anyway. Use good lighting, good technique, and it shouldn't be a problem.