Let's take one step at time, but I'll explain it in really simple terms. First you have your display profile which controls your display. Everything that follows should essentially match what you see on screen. This is why it's essential to use hardware calibration.
When you open an image in Photoshop, it should already have an embedded colour space, such as sRGB or Adobe RGB. The point about these colour spaces is that they are device independent, so if you send over a file in sRGB for example, Photoshop will know exactly how to render everything and I'll have access to the exact same information and file data as you. Assuming we both have calibrated displays the image should look very close indeed.
When you come to print, your document profile will be that RGB colour space and you should keep it that way. The change comes where you apply the printer profile, which is device specific for your combination of printer, paper and ink. This is something you can apply in the Photoshop Print Settings and then turn off all colour management in the printer, though thankfully this happens automatically nowadays on Macs.
Assuming you have a calibrated display and a decent printer profile your results should generally be excellent every time.