It has been about two years since I've last built a PC, but after a few hours of research and peer-edited lists this is the best bang-for-your-buck gaming PC build
This processor was released in the first quarter of 2017 and packs a powerful punch, even with only dual cores. Later down the road this processor will be upgrade-able to any 7th generation Intel processor (Kaby Lake) on the market, making this a safe bet.
Motherboard:
ASRock - B250M-HDV Micro ATX LGA1151 Motherboard
This motherboard supports any LGA1151 processor, DDR4 2400/2133 memory, has 1 PCIe 3.0 x16 slot and 2 PCIe 3.0 x1 slots. There are 6 USB 3.0, 6 SATA3 ports, and 1 Ultra M.2 port. It is surprisingly fully-featured compared to other Micro ATX motherboards.
Memory:
Patriot - Viper 4 8GB (1 x 8GB) DDR4-2400 Memory
It is affordable, DDR4 2400, and 8GB of RAM for $55. If you can find another stick of memory with those qualifications at a lower price I would be surprised.
Storage:
Western Digital - Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive
I recommend eventually upgrading the PC with an SSD for the Linux/Windows installation and using the Caviar Blue 1TB hard drive for storage, but on a budget, it is a great deal and with 7200RPM it won't slouch in the hard drive department.
Video Card:
Asus - Radeon RX 470 4GB STRIX Video Card
The Radeon RX 470 may be last generation's AMD card, but it is a great value. It still outperforms the 1050 Ti, and in some cases, the 1060 for almost half the cost. With a mail-in rebate, the card goes from being $168.99 to only $148.99.
Case:
Rosewill - R536-BK ATX Mid Tower Case w/500W Power Supply
Honestly, this was only because of the price and inclusion of the power supply. I recommend a better case, however, this one is small and supports the parts available. It is a great deal for what is included and looks sleek, however that is my personal opinion. Substitute this for whichever case you prefer, but this is a fantastic deal.
Power Supply:
For the sake of budgeting, the Rosewill case includes a 500 W power supply. Of course, under any regular budget, I recommend an 80+ Bronze certified power supply, however, the included one with the case fulfills the needs of this build.
June 2017 Budget Build:
The links to all of these components are below.
Complete Build Link - PCPartPicker