You can get either a wired or wireless networked printer. Seeing that most persons have internet access you will probably need a router, if you do not already have one.
For wireless printing you will need a wifi router and this will allow you to put the printer wherever you like and only be concerned with the power cord. Your PC only need be connected to the router through a wired or wireless connection.
With a wired printer you will need an ethernet cable that plugs into your router from the printer.
There are also bluetooth wireless printers as well, but that will involve you having to get a bluetooth wireless adapter for your desktop.
Only a modem is needed for broadband, not a router,
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This is obvious.
I'm recommending a router (specifically a wifi one) as many printers are now wifi capable and you will need the router to act as your networking device between the wireless printer and your computer, which should be plugged into the router.
Now if your modem has built-in NAT/router ports (or even wifi), as some companies now offer, then all that you have to do is buy a wifi printer.
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