Looking for a discrete gpu for my PC. Can anybody recommend me one? I want it for gaming. PC specs in details?

Any PCI-e 16X slot video card that draws no more power than what your box supply, whatever it is, can put on the +12VDC rail. It should have an output port or ports that can conveniently connect to your monitor or monitors. There are a few thousand different ones in the price range from $20 to $900.
That is all that can be guessed from so few details.

I'm not aware of any quad core i3's, though they do implement hyper-threading--which would show 4 threads available so I'm assuming that's what you're referring to. In general, the load of today's games will be placed on the GPU, though the i3 will start to bottleneck cards above the midrange--think GTX 960 and R9 380 as the ceiling. I don't know what games you plan on playing, but the vast majority of titles should play just fine with medium-high settings at 1080p with either of the above models on the latest AAA titles. You really can't go wrong with either pick, as they both have their pros and cons. In general, the R9 380 is shown to win in more benchmarks, but I wouldn't disregard the GTX 960. Both cards with 3rd party cooling solutions run cool and quiet though the 960 should provide plenty of room for healthy overclocking as well as offering some piece of mind in regards to driver updates for new titles as Nvidia has been shown to release updates frequently compared to AMD. You will hear people crying foul over Nvidia's last driver stumble, but NEITHER party is exempt from error so don't let that dissuade you.