Be careful - you do not want stuff up your printer and this is really easy to do with the wrong paper.
However, Google the manufacturers Web sites and you should be able to find the spec sizes your printer model will take. Do not exceed this!
With modern larger printers with a bypass or fixed input tray on the side, select the tray as the output in the printer menu. It will then give you a choice of paper types and also thickness - you can generally go easily for a thick paper or card. If you do not have the tray options do not try as you will jam the machine- the normal paper path is too complex for thick paper.
As regards other materials - as a rule no. The processes used by printers use various methods depending on if they are ink or toner, but in every case they are designed to fix the media to paper only.