4k gaming requires a custom built PC with 2 980TIs in SLI (at least).
But your budget matches.
ibuypower is decent and their prices aren't too bad. Pretty much just the basics at 2.5k, you can add fancier mice and keyboards if you want.
Gamer Paladin Z837
http://www.ibuypower.com/Store/Gamer-Paladin-Z837/W/276904
Print
Case 1 x Raidmax Horus Gaming Case-Black
Processor 1 x Intel® Core™ i5-6600K Processor (4x 3.50GHz/6MB L3 Cache)
Motherboard 1 x ASUS Z170 Pro Gaming -- 3x PCIe x16, 2x USB 3.1, 4x USB 3.0, 1x M.2, DDR4 Memory
Memory 1 x 16 GB [8 GB X2] DDR4-2400 Memory Module-G.SKILL Ripjaws 5
Video Card 1 x NVIDIA GeForce GTX 980Ti - 6GB - EVGA SuperClocked-SLI Mode (Dual Cards)
Case Lighting None
Power Supply 1 x 1000 Watt - EVGA 1000 GQ - 80 PLUS Gold; Full Modular
Processor Cooling 1 x Asetek 510LC Liquid CPU Cooling System [SOCKET-1150]-Free Upgrade to Asetek 550LC (Standard 120mm Fan)
Primary Hard Drive 1 x 256GB SanDisk Z400S SSD + 2TB 7200RPM Hard Drive
Data Hard Drive None
2nd Optical Drive None
Optical Drive 1 x LG 14x Blu-ray Re-Writer, DVD±R/±RW Burner Combo Drive-Black
Sound Card 1 x 3D Premium Surround Sound Onboard
Speaker System None
Network Card 1 x Onboard LAN Network (Gb or 10/100)
Monitor None
Keyboard 1 x iBUYPOWER Standard Gaming Keyboard
Mouse 1 x iBUYPOWER Standard Gaming Mouse
Operating System 1 x Windows 10 Home + Office 365 Trial [Free 30-Day !!!]-(64-bit) *Newest Microsoft Windows*
Warranty 1 x 3 Year Standard Warranty Service
Rush Service 1 x No Rush Service (Usually Ships in 10-15 Business Days)
Meter Display None
Media Card Reader / Writer None
iBUYPOWER Labs - Noise Reduction None
iBUYPOWER Labs - Internal Expansion None
iBUYPOWER PowerDrive None
USB Expansion Card None
Intel Smart Response Technology None
Case Engraving Service None
LED Fan Lighting None
PCI-E SSD Card None
SLI Bridge None
Subtotal $2,493.00