Try to define a logo not with cmyk values, which are relative to the color profiles and the medium which will be printed.
I'll give you an example. Do try this at home.
Take a water based marker. A cyan one.
Now draw a line on a white coated paper. Lets say a good quality magazine.
Now draw a line in a newspaper. It is the same ink, it is the same amount of ink. It is not the same color.
A color profile modifies the amount of ink depending on the characteristics of the paper (and ink) trying in the possible to have a consistent color.
Here is a diagram
You can see how converting for example the same RGB file the amount of CMYK inks changes.
The main goal is not to oversaturate the ammount of ink. In our example it would use a "dryer" marker, that delivers less ink so it does not oversaturate the paper.
So when you are using pantone values, that is converted, if needed, to a specific CMYK combination of values.
You need also to define your colors in the Coated or Uncoated pantone guide, which can vary quite a lot.
There is another part of your question:
I wish to preview on screen more closely how the logo will look
For that part you need also to have your monitor calibrated, inclusive you need to have your environmental lights controled. Take a look on color calibration tags on the forum.