NOTE: This got way longer than I expected, and I purposely glossed over a LOT of detail. If you'd like me to elaborate, just ask.
PMS Colors - Absolutely brilliant when used as designed for pre-mixed spot color offset printing. You can be assured the color you saw in your Pantone book is very closely represented in your final printed piece.
The problem is, most people don't use PMS colors for actual extra-channel spot color printing. They abuse them in a "Hey, this color looks nice" way they were never intended for.
CMYK - If you specify CMYK values in your document, you get whatever you get when it is printed. CMYK is device dependent, so just about every CMYK device will give you it's own version of that recipe.
For example, give a master chef and your mechanic a recipe for Coq Au Vin. Make sure they have the identical ingredients too. The two results are going to be different... unless your mechanic is also a master chef.
RGB - Forget about it. You have ZERO control over the device that will display your color and the possibilities are endless.
Create a new RGB document and assign the sRGB color profile. Dump in your PMS color and convert it to RGB. Use those numbers and try and stop worrying because there is so little you can do about it
Converting from PMS colors to CMYK - EVERYTHING IS A LIE. Every single conversion you find is at best an approximation. Even the official Pantone Color Bridge conversion numbers are all but useless for you, unless you are printing on the same stock, using the same inks, under the same conditions... As the Color Guide says on page ii:
"The screen tint percentages supplied are based on the printing conditions under which this guide was produced, as defined on page iii, and are intended as guidelines. If your workflow varies from ours, adjustments may be made to optimize the match."
Page iii then goes on to list the very stringent environment that most jobs are likely never, ever be printed under.
So, what do you do? Not much you can do. If you're printing spots, aka PMS colors, then your document shouldn't be combining PMS and CMYK versions of the same color.
If you're printing CMYK, then the extra spot color channels are never in play, and you're at the mercy of your printer / master chef / mechanic.
If you're displaying RGB, then you will never ever have actual printed PMS and CMYK colors in the same display.
My suggestion? Build your color guide for the branding package using Pantone's suggested numbers for RGB and CMYK. Even though they may not be correct for your specific output, at least you have the 800 pound Pantone gorilla to rely on. You used standards, and that's a good thing.
Finally, if your CMYK printer (people, not device) does "Late Binding" color management, you will likely get the best PMS color matches from their devices. Their RIP software will try to figure how to squeeze faux PMS colors out their CMYK gamut.
Follow up to user1324925less' comment. There are likely one of two things going on:
Out of Gamut - In general, the majority of the Pantone Matching System colors are out of gamut of CMYK devices. That means, no matter how hard you try, you will never, ever make a reasonable match in CMYK (just look at the Color Bridge for hundreds of examples). The CYMK color space just does not contain those colors. It's the equivalent of trying to count from 1 to potato.
You versus Them - The conversions for you are good because they are 'in gamut' and happening in your particular environment with your display, input and output profiles, your calibrated monitor, etc. When you get someone else's converted PMS colors, that happened in their particular environment which is very likely different from yours.
Either way, there will be very little you can do about. If somebody specs a PMS color, then by all intents they should be expecting to print an actual extra channel spot color, or be ready to accept the limitations of PMS conversions to CMYK.
The Pantone Matching System has become the de facto standard for "picking a color." Unfortunately, the vast majority of instances I see are abuses of PMS. People see this little booklet and think "Oh, that's the color right there!" Few realize that the color they picked is only going to happen under very tightly controlled circumstances.