Um, this is Skylake so DDR4 RAM. Stock speed is 2133MHz, not the old DDR3 1600MHz. But otherwise I agree on getting cheaper RAM if it's available and "only" hits 2133 or 2400MHz. Overclocked RAM gives you at maximum 0.5% performance boost in Skylake using a dedicated GPU in the benchmarks I've seen.
I would seriously not build a PC with only 8GB RAM for gaming right now, I'd go 16GB minimum because games are all going 64-bit and getting larger and larger.
The 960 to 970 jump in price is large, but it's without doubt the best way to get more performance.
I also wonder if there's a cheaper motherboard than the Z170-Pro available in your list. There are some Asus 100-series motherboards which are about half the price of the Z170-Pro.