It will work. The "b/g/n" part of the wi-fi you listed is a STANDARD which goes back a long time.
The only thing you'll have to do is set things up properly to ensure a secured wireless network. You also want to use the BEST security the router supports that all other wi-fi devices also support on your network (i.e WPA2 or whatever).
It's not clear why you're asking about SINGLE BAND though. As said you can Google the model. Most are 2.4GHz. I have a dual-band (2.4/5GHz) but I never use the 5GHz network since the adapters are too expensive and I can't justify it anyway since 2.4GHz is more than enough for video streaming.
(As for GAMING, I intend to use a Steam Link but I'm running an Ethernet cable since I consider ANY wireless...