Is there a CMYK palette for printing on textiles (T-shirt)?

Question

Design

Hello!
It is necessary to print a picture on a T-shirt using the "direct printing" method.
As always, the problem is in expectation (RGB on the monitor) and in reality (CMYK output on the finished product).
I understand the difference between RGB and CMYK.
I want to ask:

1. Are there conventional CMYK palettes for printing on T-shirts, or are these colors chosen empirically? With such palettes, it would be possible to set the color code to CMYK in Photoshop and not worry about how it looks on the monitor, knowing that it will look as correct as possible on a T-shirt after printing.
   
2. Is the model of the printer that is used for printing important (in theory, it should not matter, of course, because CMYK colors are the same everywhere, but you never know)?
   

Ideally, it is clear that you need to do color proofs exactly in the studio and on the T-shirt that you are going to print. But for a small circulation, this is a very large financial investment. What are the alternatives?

Answer 1

There is such a thing as hardware color profiles. The printing house can provide them to you.
Your task will be reduced to:
- calibrating your monitor with a calibrator
- inserting a color profile into Photoshop / Illustrartor / CorelDRAW / what you draw
Then the color on the monitor and the product will + - match.