First time build - $600 - Will this work?

Solution
This is essentially the same build but tweaked and I chose an Asus Mobo that will help you upgrade/OC in the future
PCPartPicker part list: http://pcpartpicker.com/p/jKbvD3
Price breakdown by merchant: http://pcpartpicker.com/p/jKbvD3/by_merchant/

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($69.99 @ Amazon)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($24.99 @ Newegg)
Motherboard: Asus Z97-P ATX LGA1150 Motherboard ($109.99 @ Amazon)
Memory: PNY Optima 8GB (2 x 4GB) DDR3-1333 Memory ($67.49 @ Amazon)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($52.91 @ OutletPC)
Video Card: MSI Radeon R9 280 3GB TWIN FROZR Video Card ($199.99 @ Newegg)
Case: Corsair 200R ATX Mid...
This is essentially the same build but tweaked and I chose an Asus Mobo that will help you upgrade/OC in the future
PCPartPicker part list: http://pcpartpicker.com/p/jKbvD3
Price breakdown by merchant: http://pcpartpicker.com/p/jKbvD3/by_merchant/

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($69.99 @ Amazon)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($24.99 @ Newegg)
Motherboard: Asus Z97-P ATX LGA1150 Motherboard ($109.99 @ Amazon)
Memory: PNY Optima 8GB (2 x 4GB) DDR3-1333 Memory ($67.49 @ Amazon)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($52.91 @ OutletPC)
Video Card: MSI Radeon R9 280 3GB TWIN FROZR Video Card ($199.99 @ Newegg)
Case: Corsair 200R ATX Mid Tower Case ($39.99 @ Newegg)
Power Supply: XFX 650W 80+ Bronze Certified ATX Power Supply ($54.99 @ NCIX US)
Case Fan: Cooler Master R4-L2R-20AC-GP 69.0 CFM 120mm Fan ($2.99 @ Newegg)
Total: $623.33
Prices include shipping, taxes, and discounts when available
 
Solution
You don't need the aftermarket cooler right away. You could probably overclock a little bit on the stock cooler if you need to compensate somewhere. As for the PSU, you could go with the xfx 550w or something. The Corsair isn't ideal, but it'll work in the system, just gotta make sure not to stress the psu too much. If you're going to do overclocking go with at least the xfx 550w if you want to add on or upgrade in the future or evga 500B at bare minimum.