what kind of printers do those menu printing and business card printing companys have?

Im really thinking about starting my own marketing company and i wanted to own the expenses. If anyone knows how much those printers cost or even the name of the printers i would appreciate it,

What kind of t-shirt printing puts the image in the shirt without being a screen with the heavy letters?

I am looking to find out how to get shirts made that dont have that bubble of the image on the shirt. Is it called a hot-press? I am looking to make a trendy vintage t shirt look.
I am looking to get t shirt made professionally, but i dont want it to be screen printed [...]