Asus ROG Strix X99 Gaming + i7 6850K = $1397
Palit GTX 1080 SJS X 2 (SLI)= $1998
Cosair 4x8Gb Vengeance LPX DDR4-2666Mhz C16 = $270
Samsung EVO 850 1Tb = $629
WD 3Tb Black = $238
SF LEADEX 1000w PLATINUM = $339
CORSAIR H115i CPU COOLER = $199
Fractal Design R5 Black w/Window = $169
Windows 10 = $150 (I think)
Total: $5239 (over your budget by $239 haha.)
All from PC Themes price list. feel free to tweak and wait for zerochaos to recommend for you. He is the Pro.
Samsung EVO 850 1 TB can be replaced with Sandisk X400 1 TB advanced TLC with ncache or Crucial MX200 MLC SSD from Amazon, easily saves you $300. All SSDs by now are sama sama. Google the reviews and you will see game loading times differ by 1-2 seconds only even when using Sammy Evos. Saving $300 can allow you to buy other things, perhaps even a PhysX card or higher end card or more storage.
WD 3TB black replace it with Seagate 2TB hybrid SSHD. The hybrid SSHD speeds up loading times significantly. Batman arkman loads in 27 seconds in 1st pass. After Seagate's onboard 8GB MLC SSD works its magic, Batman Arkam loads in a lightning 8.5 seconds on the 2nd and 3rd pass onwards, a massive improvement of 3x, and definitely in SSD territory. WD Black can't even touch the Seagate.
Don't go and buy the 4 TB Seagate hybrid SSHD. It uses a 5,400 rpm platter while the 2 TB spins at a faster 7,200 rpm. Minimum for storing apps and games, get a hybrid SSHD. Traditional hard disks do not cut it anymore.