Considering the relatively high prices and limited availability for GTX 1060s right now as a result of cryptocurrency mining, if you want a card right away, you might be better off going with something like a 1050 Ti. Even if you might need to upgrade to a new card a little sooner, you can put the money you save toward that future card. Right now, at least at US online retailers, even the lowest-priced 3GB 1060 I see in stock costs around $265, and the 6GB models start at around $315, prices that are are about $65 higher than the cards originally launched for almost a year ago. The lowest-priced 1050 Ti cards, on the other hand, start around $150, which is only a little higher than their launch price last fall.
Sure, the 1060 is notably faster, but at 1600x900, the 1050 Ti should do reasonably well in today's games at relatively high settings. And rather than waiting 3-4 years for a new card with the 1060, you could put the money you save toward getting a new card sooner, maybe in a couple years, by which time there will likely be cards faster than a 1060 for $150.
Another option, if you can, would be to wait and see if the shortage works itself out in the coming weeks or months, and hope prices get back to normal soon.
And about the 3GB 1060, in addition to having less memory, it also has 10% of its cores disabled compared to the 6GB model, resulting in about 10% lower performance even when the lower memory limit doesn't come into play. It is a fair amount faster than a 1050 Ti, but has a bit less memory, and newer games might end up running into that memory limit in the coming years, hurting performance unless you reduce graphics settings. At it's launch price of $200 it might have been an alright option, but it's now selling for more than the full 6GB version cost a month ago, which is not what I would consider a good price. It's probably a bit more "future proof" than a 1050 Ti, but it also costs around $110 more than that card at the moment.