Is this a good pc gaming build?

Solution
^Agreed. Definitely go with intel right now.
You can get windows 10 pro for $26 in some places - http://cheapdigitaldownload.com/windows-10-professional-digital-download-price-comparison/
Also added a way better power supply in my suggested build -
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-6500 3.2GHz Quad-Core Processor ($197.99 @ SuperBiiz)
Motherboard: Gigabyte GA-B150M-D3H Micro ATX LGA1151 Motherboard ($76.98 @ Newegg)
Memory: Avexir Core Series 8GB (2 x 4GB) DDR4-2400 Memory ($29.99 @ Newegg)
Storage: Samsung 850 EVO-Series 250GB 2.5" Solid State Drive ($89.99 @ NCIX US)
Storage: Western Digital Caviar Blue 1TB...

Acapella

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Jul 25, 2013
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Hey, I know you wanted under $1000, here's $1020, less after rebates. I'd recommend catching a similar monitor on sale for slightly cheaper if you're stuck to $1000. Also, speakers look a tad extraneous, but it's you not me. This Intel build will perform much better for gaming. The DDR4 memory will give a little bit of performance, and will become the standard in the future. If you're looking to cut a bit, you could go for the 6400, but again, I think there's other places you can cut that would not affect the performance of the computer.

http://pcpartpicker.com/list/frpzYr

Intel Core i5-6500 3.2GHz Quad-Core Processor - $198
Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler - $20
MSI H110M PRO-D Micro ATX LGA1151 Motherboard - $59
G.Skill Ripjaws V Series 8GB (2 x 4GB) DDR4-2400 Memory - $35
OCZ TRION 150 120GB 2.5" Solid State Drive - $40
Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive - $48
EVGA GeForce GTX 960 2GB SuperSC ACX 2.0+ Video Card - $150
VIVO CASE-V03 ATX Mid Tower Case - $45
EVGA 600B 600W 80+ Bronze Certified ATX Power Supply - $40
 

Awesomlego

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Jul 7, 2016
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I actually had a similar build planned for if I get more money than expected.
http://pcpartpicker.com/user/Awesomlego/saved/sJKFf7
 

Inkiad

Distinguished
^Agreed. Definitely go with intel right now.
You can get windows 10 pro for $26 in some places - http://cheapdigitaldownload.com/windows-10-professional-digital-download-price-comparison/
Also added a way better power supply in my suggested build -
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-6500 3.2GHz Quad-Core Processor ($197.99 @ SuperBiiz)
Motherboard: Gigabyte GA-B150M-D3H Micro ATX LGA1151 Motherboard ($76.98 @ Newegg)
Memory: Avexir Core Series 8GB (2 x 4GB) DDR4-2400 Memory ($29.99 @ Newegg)
Storage: Samsung 850 EVO-Series 250GB 2.5" Solid State Drive ($89.99 @ NCIX US)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($47.49 @ OutletPC)
Video Card: EVGA GeForce GTX 960 2GB SuperSC ACX 2.0+ Video Card ($149.99 @ Newegg)
Case: NZXT Source 210 Elite (White) ATX Mid Tower Case ($42.99 @ SuperBiiz)
Power Supply: EVGA SuperNOVA G2 550W 80+ Gold Certified Fully-Modular ATX Power Supply ($72.98 @ Newegg)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($16.88 @ OutletPC)
Wireless Network Adapter: TRENDnet TEW-805UB USB 3.0 802.11a/b/g/n/ac Wi-Fi Adapter ($22.26 @ Amazon)
Case Fan: Cooler Master SickleFlow 69.7 CFM 120mm Fan ($3.34 @ Newegg)
Monitor: Acer R240HY bidx 23.8" 60Hz Monitor ($126.49 @ Amazon)
Keyboard: Cooler Master CM Storm Devastator Gaming Bundle Wired Gaming Keyboard w/Optical Mouse ($19.99 @ Newegg)
Speakers: Genius SW-G2.1 1250 38W 2.1ch Speakers ($50.13 @ Amazon)
Other: V7 High-Performance Gaming Mouse Pad, Medium ($4.89)
Other: Wireless Optical Gaming Mouse 2.4 Ghz ($4.35)
Other: Windows 10 Professional ($26.00)
Total: $982.73
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-07-12 00:59 EDT-0400
 
Solution