PCPartPicker part list:
http://pcpartpicker.com/p/tH9cGX
Price breakdown by merchant: http://pcpartpicker.com/p/tH9cGX/by_merchant/
CPU: Intel Core i5-4690K 3.5GHz Quad-Core Processor ($229.99 @ NCIX US)
CPU Cooler: Noctua NH-D14 65.0 CFM CPU Cooler ($59.99 @ NCIX US)
Motherboard: Gigabyte GA-Z97X-Gaming 3 ATX LGA1150 Motherboard ($132.99 @ Amazon)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-2133 Memory ($76.50 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($52.92 @ Amazon)
Video Card: Zotac GeForce GTX 770 4GB Video Card ($338.99 @ SuperBiiz)
Case: NZXT Source 210 Elite (Black) ATX Mid Tower Case ($44.99 @ Mwave)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($59.99 @ Amazon)
Total: $996.36
Prices include shipping, taxes, and discounts when available
A good 4k gaming rig is going to cost more than $1000 considering you'd need to spend ~$1000 or more on video cards alone. 16gb of ram is overkill for gaming and to get 16Gb you would need to get a slower cpu or gpu which will lower gaming performance.