Building A Christmas computer

Solution
I would not recommend AMD, at this time. Dead socket, 4yr old architecture, no upgrade path. You do have the budget to get a far better system, though.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-6500 3.2GHz Quad-Core Processor ($191.91 @ Jet)
Motherboard: Asus H110M-A/M.2 Micro ATX LGA1151 Motherboard ($54.99 @ Newegg)
Memory: Team Elite Plus 16GB (2 x 8GB) DDR4-2133 Memory ($79.99 @ Newegg)
Storage: Crucial MX300 275GB M.2-2280 Solid State Drive ($70.98 @ Directron)
Video Card: Zotac GeForce GTX 1070 8GB Mini Video Card ($389.99 @ Jet)
Case: Zalman Z1 Neo ATX Mid Tower Case ($42.99 @...
I would not recommend AMD, at this time. Dead socket, 4yr old architecture, no upgrade path. You do have the budget to get a far better system, though.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-6500 3.2GHz Quad-Core Processor ($191.91 @ Jet)
Motherboard: Asus H110M-A/M.2 Micro ATX LGA1151 Motherboard ($54.99 @ Newegg)
Memory: Team Elite Plus 16GB (2 x 8GB) DDR4-2133 Memory ($79.99 @ Newegg)
Storage: Crucial MX300 275GB M.2-2280 Solid State Drive ($70.98 @ Directron)
Video Card: Zotac GeForce GTX 1070 8GB Mini Video Card ($389.99 @ Jet)
Case: Zalman Z1 Neo ATX Mid Tower Case ($42.99 @ SuperBiiz)
Power Supply: EVGA 750W 80+ Bronze Certified Semi-Modular ATX Power Supply ($59.99 @ B&H)
Total: $890.84
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-12-16 10:13 EST-0500


You can even get a better setup cheaper, if you really don't want to spend that much. That RX 480 isn't a bad GPU, but it is a good deal slower than the 1070.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-6500 3.2GHz Quad-Core Processor ($191.91 @ Jet)
Motherboard: ASRock H170 Pro4 ATX LGA1151 Motherboard ($98.88 @ OutletPC)
Memory: Team Elite Plus 16GB (2 x 8GB) DDR4-2133 Memory ($79.99 @ Newegg)
Storage: Crucial MX300 275GB M.2-2280 Solid State Drive ($70.98 @ Directron)
Video Card: XFX Radeon RX 480 8GB XXX OC Video Card ($239.99 @ Best Buy)
Case: Zalman Z1 Neo ATX Mid Tower Case ($42.99 @ SuperBiiz)
Power Supply: EVGA 750W 80+ Bronze Certified Semi-Modular ATX Power Supply ($59.99 @ B&H)
Total: $784.73
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-12-16 10:15 EST-0500
 
Solution
If you are willing to spend ~150 for cpu and ~100 for the motherboard, I would go with an intel build. I hear most AMD chips aren't at the best performance. An i5-6400 and H110 chipset is about the same price. It is a micro-ATX, but it will get the job done. I have the same exact case, and that red bar can make things a bit diffcult, but still enough clearance for decent cable management. Everything else looks pretty good to me.
 
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-6600K 3.5GHz Quad-Core Processor ($230.98 @ Newegg)
CPU Cooler: CRYORIG H7 49.0 CFM CPU Cooler ($34.88 @ OutletPC)
Motherboard: Asus Z170-P ATX LGA1151 Motherboard ($109.88 @ OutletPC)
Memory: G.Skill Ripjaws V Series 16GB (2 x 8GB) DDR4-2400 Memory ($74.99 @ Newegg)
Storage: PNY CS1311 240GB 2.5" Solid State Drive ($59.99 @ Best Buy)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($48.60 @ OutletPC)
Video Card: Gigabyte GeForce GTX 1060 6GB 6GB WINDFORCE OC 6G Video Card ($249.99 @ Jet)
Case: NZXT Source 210 (Black) ATX Mid Tower Case ($39.99 @ SuperBiiz)
Power Supply: SeaSonic S12II 620W 80+ Bronze Certified ATX Power Supply ($49.99 @ B&H)
Total: $899.29
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-12-16 11:00 EST-0500