Is this PC Build Good? | Advice

Solution
Maybe or maybe not. I chose a bit faster RAM to match the speed of the memory controller on that CPU, but if you get a 2400 MHz dual channel kit, it will only cost a few bucks more than the single stick you have chosen.
Changed the following..

1. Better and newer CPU
2. Changed RAM to a dual channel kit.
3. Changed PSU to a better quality unit.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel - Core i3-8100 3.6GHz Quad-Core Processor ($109.99 @ Amazon)
Motherboard: ASRock - B360M Pro4 Micro ATX LGA1151 Motherboard ($71.98 @ Newegg)
Memory: G.Skill - Ripjaws V Series 8GB (2 x 4GB) DDR4-2666 Memory ($80.98 @ Newegg)
Storage: Inland - Professional 120GB 2.5" Solid State Drive ($24.99 @ Amazon)
Storage: Seagate - Barracuda 500GB 3.5" 7200RPM Internal Hard Drive ($24.09 @ Newegg Marketplace)
Case: Rosewill - SRM-01 MicroATX Mini Tower Case ($26.49 @ Amazon)
Power Supply: Corsair - CX (2017) 550W 80+ Bronze Certified ATX Power Supply ($32.98 @ Newegg)
Optical Drive: Lite-On - iHAS124-14 DVD/CD Writer ($13.99 @ SuperBiiz)
Wireless Network Adapter: TP-Link - TL-WDN4800 PCI-Express x1 802.11a/b/g/n Wi-Fi Adapter ($44.89 @ OutletPC)
Case Fan: Cooler Master - R4-S8R-20AK-GP 28.9 CFM 80mm Fan ($3.90 @ OutletPC)
Total: $434.28
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-09-01 12:25 EDT-0400


Edit..

You can actually get an even better CPU within budget.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel - Core i5-8400 2.8GHz 6-Core Processor ($179.99 @ Amazon)
Motherboard: ASRock - B360M Pro4 Micro ATX LGA1151 Motherboard ($71.98 @ Newegg)
Memory: G.Skill - Ripjaws V Series 8GB (2 x 4GB) DDR4-2666 Memory ($80.98 @ Newegg)
Storage: Inland - Professional 120GB 2.5" Solid State Drive ($24.99 @ Amazon)
Storage: Seagate - Barracuda 500GB 3.5" 7200RPM Internal Hard Drive ($24.09 @ Newegg Marketplace)
Case: Rosewill - SRM-01 MicroATX Mini Tower Case ($26.49 @ Amazon)
Power Supply: Corsair - CX (2017) 550W 80+ Bronze Certified ATX Power Supply ($32.98 @ Newegg)
Optical Drive: Lite-On - iHAS124-14 DVD/CD Writer ($13.99 @ SuperBiiz)
Wireless Network Adapter: TP-Link - TL-WDN4800 PCI-Express x1 802.11a/b/g/n Wi-Fi Adapter ($44.89 @ OutletPC)
Case Fan: Cooler Master - R4-S8R-20AK-GP 28.9 CFM 80mm Fan ($3.90 @ OutletPC)
Total: $504.28
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-09-01 12:27 EDT-0400
 

Thanks for your reply! Ill take it into consideration. Also do you think not having a dual channel will make that much of a difference for his needs? He's never gonna game on this PC.