How does this look? ($600 Max)

Not bad at all with the budget in hand...Just a couple of things:

1 - If you can squeeze an SSD in, even a cheap 120GB or 240GB that will make a huge difference and one that will actually be felt...The prices are super low and with Black Friday you should find some great deals...

2 - 2 x 4GB DDR4 would be a lot better as it would then run in dual channel mode....

Also keep a look out on GPU price drops for Black Friday as there seem to be some good deals and you might just be able to squeeze a bit more value out for your friend.....
 
PCPartPicker part list / Price breakdown by merchant

CPU: AMD - Ryzen 5 1600 3.2 GHz 6-Core Processor ($129.99 @ Amazon)
Motherboard: ASRock - AB350M Micro ATX AM4 Motherboard ($39.99 @ Newegg)
Memory: Team - Vulcan 16 GB (2 x 8 GB) DDR4-3000 Memory ($99.99 @ Newegg)
Storage: Crucial - BX500 240 GB 2.5" Solid State Drive ($42.95 @ Amazon)
Video Card: Gigabyte - Radeon RX 570 4 GB Gaming 4G Video Card ($129.99 @ Newegg)
Case: DIYPC - MA08-BK MicroATX Mini Tower Case ($26.96 @ Newegg)
Power Supply: SeaSonic - S12II 620 W 80+ Bronze Certified ATX Power Supply ($34.99 @ Newegg)
Operating System: Microsoft - Windows 10 Home OEM 64-bit ($30.00)
Monitor: Asus - VP228H 21.5" 1920x1080 60 Hz Monitor ($99.99 @ Amazon)
Total: $634.85
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-11-21 13:08 EST-0500
 


The RX570 would be better but the system from SgtScream looks even better as he has squeezed a 1600, 2 x 8GB Ram a RX570..and a Seasonic power supply to boot!!! Not too sure about mini ITX....