i7 6700k, RAM, Mobo?

[iGetBSODs247]

Hi.

So Forza Horizon 3 is out but I can barely run it with my i5 3570 (non K!!) overclocked @4.20GHz and GTX 970. I mean it's lagging because the CPU isn't good enough, obviously.
If I buy a new CPU I must buy a new Mobo and RAM. But I don't know what to buy..
Currently I'm kind of leaning towards these:

MOBO: ASUS Z170 PRO GAMING or MSI Z170-A PRO (which one?)
RAM: Corsair 16GB (2x8GB) DDR4 3000Mhz CL15 Vengeance LPX Black
CPU: i7 6700k (with the fan be quiet! Pure Rock?)

Now I'm going to play games like 95% of the time and render videos and such 5% of the time.

So what Mobo and RAM do you think I should buy?
Thanks!

EDIT: so the total cost of everything is about 720 USD...
To be honest maybe it is best to upgrade the whole PC or start fresh...

 

[Vic 40]

Is the cpu at 100% all the time that you think it's the issue here? What about the gpu? Don't know the game so don't know what specs you should have,but via game dabate no bottlenencks are given. Maybe just add a 3770 for the hyper threading,it's maybe all you need?

See that the system is overclocked,did you use bclk overclocking? If so how are the ram and pcie lane working? Mean at what speeds.Keep them as close to original speeds.