Wow! How similar that is compared to my system! E8500, Gigabyte GA-EP35-DS3... Beefed up with another 4 GB to 8 GB, replaced the PSU a couple of times just in case and at least the third video card is running AH right now. And yes, the age is slowly showing. Not badly, a higher end video card (GTX970) helps a lot playing AH...
That said, with the budget you have a long living system should not be an issue.
This is just a sketch. You can save $124 by reusing your Windows license if you're going to abandon the current system. Add a $100 for a GTX 1070:
PCPartPicker part list:
https://pcpartpicker.com/list/LMqDXPPrice breakdown by merchant:
https://pcpartpicker.com/list/LMqDXP/by_merchant/CPU: Intel - Core i5-8600K 3.6 GHz 6-Core Processor ($254.89 @ OutletPC)
CPU Cooler: ARCTIC - Freezer 13 36.4 CFM CPU Cooler ($28.95 @ Amazon)
Motherboard: Gigabyte - Z370P D3 ATX LGA1151 Motherboard ($99.99 @ SuperBiiz)
Memory: Corsair - Vengeance LPX 16 GB (2 x 8 GB) DDR4-2400 Memory ($125.99 @ Newegg)
Storage: Seagate - Constellation ES.3 1 TB 3.5" 7200RPM Internal Hard Drive ($47.30 @ Amazon)
Video Card: Gigabyte - GeForce GTX 1060 6GB 6 GB WINDFORCE OC 6G Video Card ($239.99 @ Newegg Business)
Case: Corsair - SPEC-03 Red ATX Mid Tower Case ($33.98 @ Newegg)
Power Supply: SeaSonic - FOCUS Plus Platinum 650 W 80+ Platinum Certified Fully-Modular ATX Power Supply ($89.99 @ Newegg)
Optical Drive: Asus - DRW-24D5MT DVD/CD Writer ($21.57 @ OutletPC)
Operating System: Microsoft - Windows 10 Pro OEM 64-bit ($124.79 @ OutletPC)
Total: $1067.44
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-12-01 14:19 EST-0500