Either of the specifications you mentioned would work fine with a printer. The specs very the amount of twists that exist between the pairs of wires inside of the cable. Cat5 (often you'll find Cat5e) is older, and is fine for 10/100MB networks. Cat6 is rated to support 1GB networks. You will want to get a straight through cable (patch cable) in whatever version you like. Just don't get a cross over cable, this will cause you problems.
Plug your printer in, and use the software to set it up. Usually it will walk you through the setup, and it is fairly easy. Just make sure you have file and print sharing enabled on your computer so you will be able to access the printer.
Of course there is a lot more to the subject, but to answer your question that's all you really need to know.
I would like to purchase an ethernet cable to connect one end to the back of my "NETWORK READY" printer and the other end to a port on my wireless router in an attempt to set things up so I can print wirelessly from my notebook. In researching ethernet cables last night there were several different kinds; a CAT5, a CAT6, a CAT5 patch cable, a CAT6 patch cable; I'm confused and need some help here. Which cable do I need to buy to do what I want to do? Please advise if anyone knows.