The question I have is will the Intel stock heatsink suffice if I am not overclocking, and is there anything I can improve on?

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-4150 3.5GHz Dual-Core Processor  ($104.95 SuperBiiz)
Motherboard: MSI Z97 PC MATE ATX LGA1150 Motherboard  ($78.98 OutletPC)
Memory: G.Skill Ripjaws Series 8GB (2 x 4GB) DDR3-1600 Memory  ($62.99 Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive  (Purchased For $0.00)
Video Card: MSI GeForce GTX 960 2GB Video Card  ($202.98 Newegg)
Case: Corsair SPEC-01 RED ATX Mid Tower Case  ($37.99 Micro Center)
Power Supply: EVGA 500W 80+ Certified ATX Power Supply  ($20.99 NCIX US)
Total: $498.88
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-03-27 11:35 EDT-0400I would advise going for an Asus or Gigabyte board if possible, not a fan of MSI - ditto with the graphics card, I'd ditch MSI and go with another brand.

Other than that your build looks decent for your budget, if you can squeeze an SSD in there at all I would absolutely recommend it, if not maybe drop one in later.  The stock heatsink will be fine as well.  Thinking about if, if you're not overclocking (you can't with that CPU anyway) you could get a non-Z97 board to save some cash if you WANTED, but if you're planning on maybe upgrading to a K-series CPU and overclocking it later than keep the Z-series chipset.I revised it a bit.

PCPartPicker part list: http://pcpartpicker.com/p/qDHbD3
Price breakdown by merchant: http://pcpartpicker.com/p/qDHbD3/by_merchant/

CPU: Intel Core i3-4160 3.6GHz Dual-Core Processor  ($99.99 Micro Center)
Motherboard: ASRock H97 PRO4 ATX LGA1150 Motherboard  ($70.98 Newegg)
Memory: Crucial Ballistix SPORT 8GB (1 x 8GB) DDR3-1600 Memory  ($56.99 Micro Center)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive  (Purchased For $0.00)
Video Card: MSI GeForce GTX 960 2GB Video Card  ($211.99 NCIX US)
Case: Corsair SPEC-03 Red ATX Mid Tower Case  ($49.99 Newegg)
Power Supply: Corsair Builder 600W 80+ Bronze Certified ATX Power Supply  ($43.00 Newegg)
Total: $532.94
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-03-29 09:33 EDT-0400PCPartPicker part list: http://pcpartpicker.com/p/7mXdcf
Price breakdown by merchant: http://pcpartpicker.com/p/7mXdcf/by_merchant/

CPU: Intel Core i3-4160 3.6GHz Dual-Core Processor  ($109.99 SuperBiiz)
Motherboard: Gigabyte GA-Z97-HD3 ATX LGA1150 Motherboard  ($82.98 Newegg)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory  ($54.99 Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive  (Purchased For $0.00)
Video Card: EVGA GeForce GTX 960 2GB Video Card  ($192.98 Newegg)
Case: Corsair SPEC-03 Red ATX Mid Tower Case  ($49.99 Newegg)
Power Supply: XFX TS 550W 80+ Bronze Certified ATX Power Supply  ($53.98 Newegg)
Total: $544.91
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-03-29 11:19 EDT-0400