Using a large amount of your budget, I've put together a nice looking build.
Following a red and black color scheme with Cablemod custom sleeved cables, I've added a 1440p, 144Hz, IPS, G-Sync monitor, an 850w power supply for potential 1080 SLI later on, a single MSI 1080 (bit pricy, but this is following the color scheme) and some other bits and bobs.
PCPartPicker part list:
http://pcpartpicker.com/list/nzNvf8
Price breakdown by merchant: http://pcpartpicker.com/list/nzNvf8/by_merchant/
CPU: Intel Core i7-6700K 4.0GHz Quad-Core Processor ($332.79 @ B&H)
CPU Cooler: NZXT Kraken X61 106.1 CFM Liquid CPU Cooler ($114.49 @ SuperBiiz)
Motherboard: MSI Z170A GAMING M5 ATX LGA1151 Motherboard ($132.98 @ Newegg)
Memory: Corsair Vengeance LED 16GB (2 x 8GB) DDR4-2666 Memory ($85.99 @ Newegg)
Storage: Samsung 850 EVO-Series 250GB 2.5" Solid State Drive ($89.39 @ Newegg)
Storage: Western Digital BLACK SERIES 2TB 3.5" 7200RPM Internal Hard Drive ($119.99 @ SuperBiiz)
Video Card: MSI GeForce GTX 1080 8GB GAMING X 8G Video Card ($719.99 @ SuperBiiz)
Case: Phanteks Enthoo EVOLV ATX ATX Mid Tower Case ($154.99 @ Newegg)
Power Supply: EVGA 850W 80+ Gold Certified Fully-Modular ATX Power Supply ($99.99 @ Newegg)
Operating System: Microsoft Windows 10 Home OEM 64-bit ($89.00 @ B&H)
Monitor: Acer XB271HU bmiprz 27.0" 165Hz Monitor ($799.00 @ Adorama)
Keyboard: Corsair STRAFE Wired Gaming Keyboard ($79.99 @ Newegg)
Mouse: Razer DeathAdder Chroma Wired Optical Mouse ($59.99 @ B&H)
Other: CableMod E-Series Cable Kit Black/Red ($89.00)
Total: $2967.58
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-08-12 00:05 EDT-0400