If I get this, am I going to need a wireless adapter or is there an included one?
Mobo has a wired connection built in but if you want to pick up a wifi signal then yes you will need an adaptor.
edit. if gaming is a focus you might be better served by switching to an intel build as games tend to prefer their better per core/thread performance -
PCPartPicker part list / Price breakdown by merchant
tho the 4170 has now been superseded by the skylake 6100
but you need more expensive ram & mobo as well as the cpu costing more -