In general, what sizes and settings should be set for the file to print on the t-shirt? For example, to print a logo and maybe some additional text.
What else I need to know while preparing file for print on t-shirts?
This is only a technical story. It has nothing about the arty things. Hopefully you have a clear idea on what to say and by which means you can say it. You must have done some investigations on what is possible in this media (size, available colors, only short time visible, maybe partially covered, competes for attention)
In illustrator you must set
The most important thing to do soon is to get a detailed info "How the printer wants the final file to be prepared" Without that knowledge all your efforts can vapourize just because your work is not printable.
some possible fatal errors:
Online print services give reasonably detailed info.
If you use a local printer, get the quidance in email or printed. All talks is a waste of time without a document. Insist to see the physical references "this is what has gone out and this is the file preparation receipe for it"
If the printer gets arrogant and refers only to some general "all the normal customers should know that -principles", he does not earn your money.