Well these are the oculus rift requirements, HTC vives are similar. My rift ran ok on a GTX 980 which is not too different from the 1060, the 6gb version would be safer but you should be ok. You are at the low end of requirements though.
Video Card: NVIDIA GTX 970 / AMD R9 290 equivalent or greater.
CPU: Intel i5-4590 equivalent or greater.
Memory: 8GB+ RAM.
Video Output: Compatible HDMI 1.3 video output.
USB Ports: 3x USB 3.0 ports plus 1x USB 2.0 port.
OS :Windows 7 SP1 64 bit or newer.
Likely depends on the headset you're wanting to run. More than likely, your system will run any of them, but performance will likely vary. For the record, my system (see my sig block) runs the Lenovo Explorer well enough for me, though I will be upgrading to a GTX 1060 this week.