computer build budget but enough graphics to run game optimal or?????

[Shokun]

Well that's a budget. Depending on area the ps4 goes for 390$ - 390€, gonna be a tough nut to crack. But let's see. (I'm gonna assume here that you either have a display and peripherals, or you would need to buy them with ps4 too so not included in budget). I'll try to make the build with U.S. prices, for euros just change symbol and you'll be close.

Full build in PCPartPicker:
http://pcpartpicker.com/p/FBthHx

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PCPartPicker part list: http://pcpartpicker.com/p/FBthHx
Price breakdown by merchant: http://pcpartpicker.com/p/FBthHx/by_merchant/

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($64.89 @ OutletPC)
Motherboard: Gigabyte GA-Z97-HD3 ATX LGA1150 Motherboard ($79.89 @ OutletPC)
Memory: Crucial Ballistix Tactical Tracer 8GB (2 x 4GB) DDR3-1866 Memory ($36.99 @ Newegg)
Storage: Hitachi Ultrastar 750GB 3.5" 7200RPM Internal Hard Drive ($34.99 @ Amazon)
Video Card: EVGA GeForce GTX 950 2GB Superclocked+ ACX 2.0 Video Card ($129.99 @ Newegg)
Case: Cooler Master Elite 430 ATX Mid Tower Case ($25.00 @ Newegg)
Power Supply: Corsair CX 500W 80+ Bronze Certified Semi-Modular ATX Power Supply ($34.99 @ Newegg)
Total: $406.74
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-10-17 13:11 EDT-0400
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It should have enough power to run games smoothly, without breaking the bank. It's also skipping most extras that might affect performance (like SSD), but it's easy to upgrade it later. If you want to save more, the motherboard can be downgraded, I chose this one because it was the cheapest Z97 chipset available which supports overclocking. Other road (more recommended in the long run imo) is to upgrade from stock cpu cooler to aftermarket one and overclock it, I hear this CPU is a beast overclocked (even with stock cooling) so the build has a lot of potential considering you most likely want to use it as long as possible.

Skipping the extras allowed me to put a bit more on graphics, which is the most important part for gaming (I'm not saying less isn't enough, but more is better and more future-proof). GTX950 is best bang for buck at this time, hands down. If you want to save here, next card below would probably be GTX 750 ti.

It's a bit more than what one would pay for a PS4, but I think this is more long-lasting investment than PS these days.