In order to achieve the best match possible you need the following
1. Calibrate and profile your monitor.
For that you have your ColorMunki. ColorMunki profiling software will generate a monitor profile for your monitor. This profile should be assigned as your default monitor profile in Windows. It is quite possible that after generating the profile ColorMunki software will do this assignment for you. If not, you can easily do it in Windows color management settings.
Note that this step does not in any way involve Costco and their profiles. This is entirely between you, ColorMunki and your monitor.
2. Use color-management-aware software to adjust your photos on your monitor to make your photos look the way you want them to look. Adobe Photoshop, Adobe Lightroom, Corel PaintShopPro, Corel Paint - all will do. I assume Faststone image viewer/editor is also color-management-aware.
3. Use calibrated and profiled printing service. Now, I never used Costco myself, so I don't know how it really works with them. But typically there are two possibilities:
3.1. Printing service uses "smart" color-management-aware software and printers to print images.
In this case you don't have to do anything at all. Just send them your files after making all desired adjustments, and they will reproduce them on paper as faithfully (as close to the original) as possible. All color-reproduction related adjustments will be done by the printing service internally.
3.2. Printing service uses "dumb" machines and software to print images. They don't perform color-reproduction related adjustments.
Now, this is not necessarily the end of the world. Printing service that uses "dumb" machines might still decide to profile their "dumb" machines and make the resultant color profiles available to the public. You are supposed to download that color profile. And you are supposed to convert your image files to that color profile before sending them to printing service. Profile conversion is available in Adobe Photoshop through "Convert to profile" command. I expect that Faststone also has this capability.
Note, that this latter procedure will modify your images. You should make copies of all your images and apply this conversion to the copies. It is these converted copies that you'll send to printing service. It is possible that these converted images might look "strange" on your monitor and their color reproduction might look wrong to your eye. This is OK. The whole idea of these conversion is to "distort" your color in that specific way that will precisely cancel out distortions introduced later by the printing machine. If the color profile distributed by the printing service is good (properly describes the machine), then this technique will let you to obtain correctly colored images from "dumb" machine.
3.3. Printing service invented a third, alternative, unorthodox way to handle color management.
So, judging by the fact that Costco distributes their color profiles, I'd guess that they expect you to follow procedure 3.2. But I could be wrong, since as I said above I never used Costco myself.