First time build, Minecraft.

Well only too glad to help another dad.

Minecraft is not a heavy requirement game so we should be able to do something in that price range.

The system below includes everything you need including Win10 home.

In this system I have chosen not to include a discrete video card but to rather rely on the integrated graphics on the CPU for the time being. The Game Debate website lists the GeForce 8600 GS video card as recommended,
http://www.game-debate.com/games/index.php?g_id=1235&game=Minecraft

The Intel HD 630 graphics on the G4600 CPU is hugely faster than the 8600 GS
http://gpu.userbenchmark.com/Compare/Nvidia-GeForce-8600-GS-vs-Intel-HD-630-Desktop-Kaby-Lake/m11015vsm178724

Next issue here is that I do not know what kind of connection your monitor has. The MSI - B250M MORTAR motherboard has 1 x DVI-D, 1 x D-Sub and 1 x HDMI1 connector.
https://www.asus.com/ca-en/Motherboards/PRIME-B250M-A/specifications/

If you are not sure about the connection type here is a link to help explain
http://www.expertreviews.co.uk/accessories/pc-monitors/1404476/hdmi-vs-displayport-vs-dvi-vs-vga-every-connection-explained

This system is based on it upgrade capability. You can get a fairly decent gaming system here by adding a discrete video card, a good choice would be a GTX 1050 or GTX 1050 Ti or RX 560. You can even go as high as a GTX 1060-6GB or go as low as a GT 1030. It all depends on what you want to play.
https://pcpartpicker.com/products/video-card/#c=396,379,380,373,395&X=100,889900&sort=price&page=1

You can also upgrade the CPU, here is a list of supported CPU's and another with pricing. You would have to move to an i5 CPU to see a significant improvement
https://www.asus.com/ca-en/Motherboards/PRIME-B250M-A/HelpDesk_CPU/
https://pcpartpicker.com/products/cpu/#X=100,408395&sort=price&s=12,13

Don't worry about overclocking, it is the computer world's version of building a drag racing car. You can get by without it and this system won't anyways.

Last, you might want to look around for your copy of Win10. The one I chose below is the OEM version, which means that it can only be installed on one machine and cannot be later transferred to another machine. A full version will cost you about $10-$15 more but can be installed wherever you want and transferred as many times as you want.

PCPartPicker part list: https://pcpartpicker.com/list/FRmBNN
Price breakdown by merchant: https://pcpartpicker.com/list/FRmBNN/by_merchant/

CPU: Intel - Pentium G4600 3.6GHz Dual-Core Processor ($86.99 @ Newegg)
Motherboard: Asus - PRIME B250M-A Micro ATX LGA1151 Motherboard ($76.98 @ Newegg)
Memory: Crucial - Ballistix Sport LT 8GB (2 x 4GB) DDR4-2400 Memory ($91.99 @ Newegg)
Storage: Seagate - BarraCuda 1TB 3.5" 7200RPM Internal Hard Drive ($44.99 @ Newegg)
Case: Deepcool - TESSERACT BF ATX Mid Tower Case ($40.98 @ Newegg)
Power Supply: SeaSonic - S12II 520W 80+ Bronze Certified ATX Power Supply ($51.98 @ Newegg)
Operating System: Microsoft - Windows 10 Home OEM 64-bit ($112.98 @ Newegg)
Total: $506.89
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-12-05 14:12 EST-0500