Wireless printers connect (wirelessly, of course!) to your router. They can then accept printing instructions from any device connected to that router (such as a PC, laptop or tablet), irrespective of whether those devices are connected to the router wirelessly or with Ethernet cables.
(Some wireless printers can also connect
directly to certain devices, without going via a router, but that's not relevant here).
However almost all wireless printers offer USB connection as an alternative, so you don't have to use the wireless option if you don't want to.
It's worth spending a little extra to buy a printer that uses separate cartridges for each colour, rather than a printer that has all of the colours in a single cartridge; it will save you far more money in the long run. The explanation for that, together with my recommendation for the printer you should be taking a look at (the Canon Pixma MG6450) can be found in my posts here:
http://www.theanswerbank.co.uk/Technology/Question1422985.html