It is important to understand what a color profile is. And the diference to color spaces, that is diferent.
What calibrating a monitor is?
The basic idea is that specialized hardware measures a series of controlled color patches to see what the monitor is capable of displaying, and comparing the real output of the monitor versus the color that should have displayed, make some adjustments, to pump the color or diminish it.
This makes a profile for the monitor in its current conditions. This profile is normally stored to be used by your operating system in general, not an aplication.
And whow about calibrating a print?
Then you sent to print a secific file with specific series of patches. Then again you measure them and the program make some adjustments to the specific printer profile, to even pump some ink more or make it dimmer.
(You will be asked to print the same file again and you will see the diferences)
This profile is placed in a folder that specific programs like Photoshop, Corel, Indesign and Ilustrator can use for a specific case.
There are generic profiles for some circumstances, for example Swop, Gracol, Eurocoated, Japan, Fogra. If you do not have aspecialized hardware you should use the most suitable profile with it specific variations (Coated, Uncoated, etc.)
You need to investigate a little bit what profile you need... or your provider is using.
Digital and home user
Normally you just want to use a generic RGB color profile... In reality you need a generic Color Space. (but that is out of the scope of this answer). The most commonly used is sRGB, Adobe 1998 and ProPhoto.
And let the printer software do the proper calculations.
Previewing the print
But let us imagine that your red gives its best effort to be bright but simply can not. Then this information is sent back to the color profile so, when you see the preview on your monitor you do not see the unreal bright red, but a simulation of the actual red your print made.
So the best practice is to calibrate your monitor and printer exprofesso.
On a print it specific to the ink-paper-process combination and specific to a CMYK output. This does not apply to spot colors.
Spot colors are simulated internally by the aplication (Photoshop, Ilustrator, Corel, Indesign)
The calibration does not depend on the motherboard. Depends on the graphicsCard-monitor-operatingSystem combination.
And also the environment. Take a look at this post: https://photo.stackexchange.com/questions/85499/display-calibration-for-viewing-on-displays-devices/85501#85501
Adjusting Gamma on a monitor is a poor man´s aproach, that can render decent results. Take a look at this: How configure color in InDesign for a specific printer?
Regarding contrast and brightness, totally depends on your monitor, viewing conditions and that suits you. The calibration software might give you some instructions. This is affected by the enviroment light.