printing setting

One of the things you want to ensure is that you are not accidently using two color management systems, which can be a common issue. As you mentioned, you'll use Photoshop Manages color, but make sure that you turn off color management in the print driver.

The rendering intent will depend on your image and out of gamma colors.

Please feel free to ask specific questions.

Best

I use Epson. Remember if you have PS manage colors, you must turn off "printer manages color"  in your printer driver so you don't get double management.  Weird colors.

Photoshop manages colours-->switch off colour management of the printer.

The very first and most important thing with printing is: Does the result please you or not? If yes, no need to ask more questions. If no, you need to investigate the cause.

For that you may come back with your questions by pointing out the specific problem.

Most people doing home printing will use a color profile such as sRGB or Adobe RGB so there is really no need to worry as the Photoshop default will be relative colorimetric. So I would recommend leaving the default setting unchanged for photography and multicolour artwork. However if you are using a special print profile that may incorporate a rendering intent.

Relative takes into account the white point; useful where the final output is white photographic paper. The difference between relative and perceptual is how out of gamut colors are adapted. For a technical explanation see this link.

https://www.cambridgeincolour.com/tutorials/color-space-conversion.htm