Graphic Design

Illustrator is best for graphics that are Vector format

https://helpx.adobe.com/photoshop-elements/key-concepts/raster-vector.html#:~:text=Raster%20(or%20bitmap)%20images%20are,for%20rendering%20the%20image%20elements.

Photoshop can also create Vector graphics but it's limited and requires to save the file as PDF with all vector elements in tact.

And Photoshop is mainly for Photo manipulation. It's not a design tool. Although a lot of people can and do use Photoshop to design, which is completely fine.

InDesign is a Page Layout Programme. 

It can contain both Vector and Raster elements. You can Place an Illustrator File or a Photoshop File into your layout and manipulate the design layout and elements.

All three would be valid ways of creating t-shirt designs.

All three have limitations and require a working knowledge of the t-shirt printing process and also how each program is beneficial to your design goals.

There's a few courses you can do - LinkedIn Learning has a Months free.

https://www.linkedin.com/learning/learn-t-shirt-printing-and-design

This should give you a good overview of the process.

And where you need to go from here.

Can you tell us more about your potential designs. The more the better.

Photoshop may be the better choice if you are mainly manipulating images. Illustrator may be the better choice if you are creating logos and/or patterns.