I'm building a computer for the first time, its main function will be gaming, and for now I'll just use one monitor. Will I need a 4gb or a 6gb graphics card?
If you're gaming at 1080p, 4GB will be just fine.
I would suggest that you link you build here so the guys can advise you on the complete solution.
I've been using 4gb and its working fine. But if you can afford a 1060 6gb that would be a good option imo. Especially since you say its for gaming.