1) For Skylake such as the i5-6600K you would use DDR4
(there are DDR3 boards for Skylake but DO NOT GET ONE as it can easily destroy your CPU).
2) DDR3 is for Haswell such as the i5-4690K (i.e. Asus Z97-A motherboard, 2x4GB DDR3 1866MHz CAS9 kit memory)
3) 16GB vs 8GB: the amount depends totally on what you're doing. You won't benefit currently from more than 8GB for gaming but unless you have a tight budget I'd suggest 16GB (2x8GB kit).
So...
I suggest rephrasing your question as suggested. Such as:
"I'm building a gaming build and have $800USD for the case and internal hardware... what's the best choice?"
People can put together a build using pcpartpicker to balance the parts for you.
(Note that Skylake is more expensive. I...