DPI (Dots per inch), which is the resolution/detail that the printer can print.
Paper size, as you may want to print on a large range of media
Paper type, as conventional printers would print on standard paper, whilst different uses, such as photography, would benefit from printing on higher quality photo paper.
Connectivity, this can range from wireless over WiFi or Bluetooth, wired over Ethernet or USB, or even where you may have to connect a USB/SD card directly into the printer. All of these data transmission solutions would result in their own constraints and benefits.