Adobe illustrator does not have L*a*b* color, and I'm trying to create a color palette for my company, and I want to know which of the 3 values Illlustrator uses will give the most consistent color. I'm assuming HSV is most consistent, and will translate to L*a*b* more accurately than RGB or CMYK, but I may be wrong.
HSV is a color editing tool, it's not a color model. You can edit a CMYK or RGB color with the HSV option. It doesn't change whether it's an RGB or CMYK color.
You need RGB for anything on-screen.
You need CMYK (or spot) for anything to be printed.
If you want consistent color, specifying a spot color would be your best option. Then translating that spot color to RGB and CMYK values.
In short, you can't just pick one color model for all media/devices. You have to specify colors based on their end use.