Question really can't be answered without monitor resolution. Assuming 1080p, the 3 GB 1060 is just fine. Note that the amount of memory is not the only difference between the cards. The 3 GB model has 1152 shaders compared to the 1280 on the 6 GB model. Jumping up to the 6 GB 1060 w/ 1280 shaders will bring you about 7% more speed. If ya wait a week or 2, you should be able to get the 6GB model for the 3 GB price as stores start to have sufficient stock on the AMD 5xx cards, prices can be expected to drop a bit more.
The newer models w/ faster memory speeds are not really bringing much to the table... the MSI 1080 for example, gets manages a 4% fps increase in overclocked speed.... so if the price premium is much more than that, you might wanne grab one of the older ones.