If the printer is "Wireless" than the router must support that.
I use a mix here. I have one computer wired, The printer is wired, Two DVR's are Wired (And toss the odd gig of data between them) and another computer that can be either wired or wireless depending on where it's parked, I hope to get more (Dedicated job) computers over the winter, Plus two Android devices (Wireless) Internet access IS a factor for me.. It is provided by a Linksys WiFi "Modem" like adapter.. The router thinks it's a cable modem.