Well I voted for options 1 & 2 since I think a combination of both would help the most. Without using flash, you're going to have a tough time with the variable minimum aperture of that lens inside. I never use flash but I also rarely shoot above a 2.8 aperture inside unless the light is really good (like on a bright sunny day) and that's with my ISO pretty high. I'm always willing to trade grain for sharp photos but not everyone is.
I don't think you necessarily need to shoot in manual mode but you should learn how ISO, aperture and shutter speed work together so you understand what your camera is doing in auto or even P mode. I like to use Aperture Priority mode since it lets me set the aperture and then adjust my ISO based on the metered shutter speed which helps a lot in low light. It's really not about which setting you use as much as understand what's actually happening with the settings the camera chooses.