Casey W. answered 04/24/23
Experienced Agency Owner with 25 years Graphic Design Experience
The best color profile to start with in Illustrator when designing a logo for web and print for me usually depends on where it will be seen most, but univerally, CMYK is the best practice. Personally, I want to have full options available to me for the web though to start. You can always work in RGB mode and then convert to CMYK for print, but of course watch out for the dreaded blue to purple shift when converting blues for print, (ask my how to avoid this).
It is not necessary to work on them in two different files. The color profiles can be managed within the same file. It is important to make sure your color profiles are set properly and consistent across all your design work.
Regarding the issue of color values jumping around, this is likely due to color management settings. Make sure to turn on color management policies for both RGB and CMYK. You can also use a color management software like ColorMunki or X-Rite to calibrate your monitor and ensure accurate color representation. Finally, it's a good idea to create a color proof for print to ensure that the final product matches your design intent.