Tried to get the best build I could under the budget. Its skylake/pentium based and quite certainly reflects some of my build biases. Its designed to be a simple machine with relatively few compromises and the option to upgrade as funds are available. @ivaan's machine is probably another useful starting point though I went for slightly more modern, smaller parts. I've linked the PC parts picker list so you can play around
PCPartPicker part list: http://pcpartpicker.com/p/Yy3XjX
Price breakdown by merchant: http://pcpartpicker.com/p/Yy3XjX/by_merchant/
CPU: Intel Pentium G4400 3.3GHz Dual-Core Processor ($59.99 @ SuperBiiz)
Motherboard: ASRock H170M-ITX/DL Mini ITX LGA1151 Motherboard ($92.98 @ Newegg)
Memory: G.Skill Ripjaws V Series 16GB (2 x 8GB) DDR4-2400 Memory ($74.88 @ OutletPC)
Storage: Hitachi Deskstar 7K2000 2TB 3.5" 7200RPM Internal Hard Drive ($62.00 @ Amazon)
Video Card: Asus GeForce GTX 950 2GB Video Card ($139.99 @ Micro Center)
Case: Cooler Master Elite 110 Mini ITX Tower Case ($38.98 @ Newegg)
Power Supply: *Cooler Master Elite Power 400W ATX Power Supply ($29.99 @ Directron)
Prices include shipping, taxes, and discounts when available
This is a starting point. Its useful to understand why I picked certain parts, and what you can replace them with
So... compromises - I went for the lowest end pentium I could, for low cost and power efficiency. A proper core i3 or i5 would be nice. I went with skylake since there's a few useful features
I went for 16gb of ram, personal bias, and you could save a few dollars going for less, but this maxes out the ram. Depends on your needs but 2x4 would work. This is DDR4 ram, rather than DDR3
Asrock's reasonably solid these days, and a mini itx motherboard/case is about as small as you can go and still game. This one's wierd and dosen't support m.2 but I was trying to minmax for cost+trustybrandedness.
Went for a mini itx compatable small video card - maybe a 960 or a r9 nano would be a step up.
The cooler master Elite 110 is a nice small case that takes a full size PSU. I find small form factor PSUs limiting.
The PSU is a compromise for cost. I'd much rather a modular PSU in a mini ITX build .
I'd use stock cooling here - its good enough, small, and I have not much of a budget to design off of.
HGST is basically the most reliable consumer hard drives you can buy. Its not that much more, and I trust them. I guess you could swap this for a SSD or a smaller drive.