If your home does not already have a wireless router, than obviously you'd have to set one up. (Depending on the quality of the wireless adapter, if your router is far from the rig, you may want a repeater or additional router.) A USB wireless adapter should work fine. Mining does not require much bandwidth; the main things are reliability and latency.

Ethernet is typically more reliable and offers lower latency (and hopefully fewer stale shares, where another miner "beat you to the punch"), in most cases. Usually the difference is negligible, unless one of them happens to be very poor.