OK, here is a strategy. Figure out the lowest cost system you could build, then see what is left over for the graphics card. The MB will have to match/support the graphics card pci version (pci-express 2.0, 3.0, etc.), and the power supply will have to support processor and graphics card; at a given performance level, the more power-hungry CPUs are somewhat less expensive (ie, a 125 watt will be less than a 90watt at equivalent performance level).
Where can compromises be made? Others will disagree, but I would go cheap on the case, find a budget power supply with good ratings, and find a basic but well-reviewed motherboard. Arguments for spending a lot on a case are mainly that a good case allows good air flow, and is quieter.
Well, as along as the system chip and CPU stay cool, which is almost guaranteed as long as you build normally, the role of the case in cooling is very small. So, that is why I say go cheap on the case. As for power supplies and motherboards, there are great ones at low prices; paying more just gets unessential features, although a cheap power supply that is not well-reviewed can be cheap in a very bad way.
For MB, you do want pci express 3.0 / x16 capability.
You can go very cheap on hard drive by opting for hard drive versus SSD. The speed of SSD is just too good to pass up, though, and you can get SSDs with good capacity for not much money. Again, look for reviews to see what is recognized as good.
For RAM, Techspot reviewed 4gb 8gb versus 16gb for gaming, and found negligible difference.
https://www.techspot.com/article/1043-8gb-vs-16gb-ram/page3.html
So, yet another place to budget is on RAM.
Tom shar dware reviews processors at different levels, and likes the AMD FX-8300. cp uben chma rk dotcom reviews "cpu value," price for performance.
They note FX-8350 as strong. It is priced better than the 8300 at ne we gg.
I looked for well-reviewed components (at ne we gg) to complete this, up to but excluding vid card.
$160 CPU
$075 MB: gigabyte GA-970A-D3P sata 6gb/s, USB 3.0, pci x16
$020 RAM team elite plus ddr3 1333 4gb (can be overclocked)
$060 case, power supply: Rosewill I5-397-BK with 450 watt psu
$040 Silicon Power S60 120gb sata III ssd MLC
$100 operating system
___
$455.
$600 - $455 = $145.
Now, go check out reviews of vid cards and see what you can get for $145. It takes a lot of shopping, since there are a few parameters to look at all at once. A card in this range will likely draw about 150 watts; the CPU noted is 125 watts. Together, that is 300 watts, and another 100 watts should be fine to power the rest of the system.
One card idea: $135 - MSI Radeon R7 370 256-bit GDDR5.
