Here is a lower level recommendation that reduces the CPU and Motherboard while keeping quality components for the rest.  Started by Ken's original recommendation for the processor and motherboard but with an attempt to upgrade memory and video.
Intel
CPU: i3-4150 3.5GHz Dual-Core ($121 @ DirectCanada) (CPUBenchMark 5050) 54watts
MB: Socket LGA 1150 (Asus, ASRock, EVGA, Gigabyte, MSI), 2 RAM slots, Max RAM 16GB+ ($45-$65)
AMD
CPU: AMD FX-4300 3.8GHz Quad-Core ($120 @ Vuugo, NCIX, DirectCanada) (CPUBenchMark 5254) 95watts
MB: Socket AM3+, (Asus, ASRock, Biostar, Gigabyte, MSI), Max RAM 16GB+ ($57 - $75)
I know you earlier mentioned disinterest in MSI but I have used a couple of their motherboards in the past with good results.  They create stable motherboards for the inexpensive and low end of options with no overclocking.
Video Card:
GTX 750 Ti ($140 - $200)
R9 270 ($160 - $202)
R9 270X ($180 - $260)
Memory: 1600MHz (1x8GB) CL9 1.5v ($95)
SSD : 128GB for OS ($65)
HDD : 1TB for files and games (7200 or slower rpm) ($65)
Case & PSU: ($120)
Operating System: MS Windows 8.1 64bit ($100)
Total: $445 + CPU + MB + video = $445 + $180 = $625 + video = $625 + ($150-$200) = $775 or $825
Costs can be reduced in the Case & PSU, I figured $60 for each but purchasing a combination would be cheaper than individually.
The total cost is still reaching $800 even with a lower cost cpu & motherboard.  The video card can be knocked down to a $100 or $125 card.  The memory can be knocked down to 4GB.
Other possibilities are Ken's original recommendation in Post #2, Combo Deals, Pre-Built OEM such as Dell or HP, or upgrading what you have.