Using a printer will save your staff a lot of time. They won't have to check a tablet or transcribe orders to tickets.
Printer must be connected to the same network as the tablet. You should assign your printer a static IP on your network it is the most reliable way to connect your printer.
Ethernet connection. There are wi-fi models of the printers below. They are really hard to set up, more expensive, and not as reliable as an ethernet connection. Run the cable to your printer and save yourself a headache. WIRELESS PRINTERS ARE NOT SUPPORTED.
Paper & Ribbons. You will need to think about keeping printer paper in stock (and potentially ink ribbons) depending on what printer you purchase. The printer can't print without them.
Star Micronics TSP143IIILAN (recommended)
This is a thermal printer so it does not require you to purchase an ink ribbon. It prints using heat. Note: High temperatures in the kitchen can impact thermal paper.
Star Micronics SP700
Either of these printers should work. You are welcome to conduct your own research on which one is better. It might be worthwhile talking to a Star Micronics directly and purchasing through them because they may be able to provide better hardware support.