Much depends on the particular games you play.
Most games depend on the single fast master core for performance.
sims, strategy and mmo games fall into that category.
Few games can make use of more than 2-3 cores.
But, sme games, like multiplayer with lots of participants benefit from many cores.
fast action shooters will depend more on fast graphics.
With no budget limitations, the i5-6600K with an overclock is arguably the best gaming processor.
But, you are looking at twice the cost of a i3-6100.
If your budget is less than that, I would vote for the i3-6100 as one of the best budget processors.
Look at the newegg reviews if the i3-6100 from verified buyers. You will be surprised ant how many different gaming setups are served well by this chip.
Do spend a bit more for a Z170 motherboard.
That will preserve your option to upgrade to a "K" processor and overclock.
It also will support the upcoming kaby lake processors.