Only a retard would take an I3 processor for gaming lol.
People on tight budget would, and it's efficient enough

AMD AM3+
Motherboard: Gigabyte 990XA-UD3 / Gigabyte 78LMT-USB3 (rev. 6.0)
CPU: FX-8320E / FX-6300
Intel 1150
Motherboard: Asus Z97-P (1150) / Asrock Z97 Anniversary (1150)
CPU: Intel Core i5-4460 (1150) / Intel Core i5-4590 (1150)
Intel 1151
Motherboard: Asus Z170-P / Gigabyte Z170-HD3P
CPU: Intel Core i5-6600 / Intel Core i5-6400
RAM: 4GB / 8GB Kingston ValueRam (cheap & good)
PSU: Anything 500w/600w but good brand. (Ex; Corsair, ThermalTake, CoolerMaster, XFX, EVGA)
HDD: In my country 500gb to 1tb is like 10 euros difference, up to your budget, save for an SSD later.
Case: For budget you do not mind the appearance, but the fans.
Fill the prices on those, because I have no idea where you shop/live or what you can find.
In Greece; following components I gave you earlier that'd be;
Asus Z170-P > 125Euros
Intel Core i5-6400 Box > 200Euros
Kingston 4GB DDR3-1333MHz (KVR13N9S8/4) > 20Euros
Toshiba DT01ACA100 1TB > 45Euros
Corsair VS Series VS550 80Plus > 50Euros
<440 Euros until now>
Gigabyte Radeon R9 380 4GB > 230 Euros
+Case + DVD = total of 700 Euros.
You can always go with AMD Build which comes better to budget.