Overall, how would you rate my hypothetical build? (Looking for opinions and criticism.)

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You could get an i5 with a new R9 380 for only a few dollars more. Way more powerful system than 6300 and 260x.
Change the case to the mid-tower you want.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4460 3.2GHz Quad-Core Processor ($176.95 @ SuperBiiz)
Motherboard: ASRock H97 Anniversary ATX LGA1150 Motherboard ($69.89 @ OutletPC)
Memory: G.Skill Sniper 8GB (2 x 4GB) DDR3-1600 Memory ($48.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($44.99 @ Amazon)
Video Card: Sapphire Radeon R9 380 2GB Dual-X Video Card ($203.98 @ Newegg)
Case: Deepcool TESSERACT BF ATX Mid Tower...
I recommend getting an aftermarket CPU cooler since AMD CPUs easily heat up to higher temperatures. The Cooler Master Hyper 212 EVO, Hyper 212 Plus, and the Hyper TX3 are all great CPU coolers. Otherwise, it's a solid build.
 
You could get an i5 with a new R9 380 for only a few dollars more. Way more powerful system than 6300 and 260x.
Change the case to the mid-tower you want.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4460 3.2GHz Quad-Core Processor ($176.95 @ SuperBiiz)
Motherboard: ASRock H97 Anniversary ATX LGA1150 Motherboard ($69.89 @ OutletPC)
Memory: G.Skill Sniper 8GB (2 x 4GB) DDR3-1600 Memory ($48.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($44.99 @ Amazon)
Video Card: Sapphire Radeon R9 380 2GB Dual-X Video Card ($203.98 @ Newegg)
Case: Deepcool TESSERACT BF ATX Mid Tower Case ($40.98 @ Newegg)
Power Supply: Antec EarthWatts Green 650W 80+ Bronze Certified ATX Power Supply ($64.99 @ Amazon)
Operating System: Microsoft Windows 8.1 OEM (64-bit) ($87.88 @ NCIX US)
Wireless Network Adapter: TP-Link TL-WN881ND 802.11b/g/n PCI-Express x1 Wi-Fi Adapter ($17.99 @ Amazon)
Keyboard: Microsoft Desktop 400 Wired Standard Keyboard w/Optical Mouse ($18.03 @ Amazon)
Total: $774.67
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-06-20 17:01 EDT-0400
 
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