The 3 GB version of GTX1060 will run AH3 very well on a single 1920x1080 monitor with most of eye candy enabled.
If your itch isn't too bad, I'd recommend you to wait to get the Alienware for $500 cheaper. Or, if you're willing to pay the higher price, you'd get a much better performer for years to come.
However you said you'd need a monitor, too... Have you thought about maybe getting one of those ultra wide curved monitors? Or even 4k? Or 144 Hz? Or even a combination of those? If so, then the 1060 won't be enough. In that case the Best Buy option would be a Worst Buy way too soon.