@Dalton (I stink at names) Ok so I'm going to go a bit over your budget and I'll explain later why.
Now for the processor I went for either http://www.newegg.co...N82E16819116898 or http://www.newegg.com/Product/Product.aspx?Item=N82E16819116899 the difference between the two of them is that you can overclock the 4670K (Overclocking basically means you push the frequency beyond what the manufacturer intended, basically it will run faster).
For the motherboard : http://www.newegg.co...N82E16813128629
The video card : http://www.newegg.co...N82E16814130932
Memory: http://www.newegg.co...N82E16820104338
The case: http://www.newegg.co...N82E16811553013 or http://www.newegg.com/Product/Product.aspx?Item=N82E16811352026 now the case doesn't really matter that much because it doesn't increase the performance of your PC but more expensive cases have features that will make your life easier. For example it may have removable dust filters or better cable management or it has acoustic foam to reduce the overall noise the PC makes. The case depends on the preferences of each individual.
The power supply: http://www.newegg.co...N82E16817139048
Storage: Here you have two options you either go for an SSD http://www.newegg.co...N82E16820211718 and you use it for Windows and programs and you get a Hard Drive http://www.newegg.com/Product/Product.aspx?Item=N82E16822236339 for your games, music, movies, etc. Or you can get just the Hard Drive for everything including Windows. The differences between an SSD and a Hard Drive is that a HDD is cheaper and slower because inside of it there are moving parts, the SSD is faster and more expensive also it has no moving parts. I can give you more details but it will just confuse you.
The monitor: http://www.newegg.co...N82E16824001792 or http://www.newegg.com/Product/Product.aspx?Item=N82E16824005363 The Samsung has a TN panel which means decent viewing angles and decent color accuracy, now the LG uses an IPS panel meaning it has better viewing angles and the colors are accurate.
Optical Drive: http://www.newegg.co...N82E16827151266
Now depending if you go for the cheapest components I selected when it came to the processor and the case and monitor and storage. It will cost you about 940$. If you go for the better monitor, case, SSD and HDD combo it will cost you about 1080$.
Notice that I didn't include a mouse and keyboard because maybe you already have them and you can still use them and if you don't have a mouse and keyboard, they are not that expensive. Also when it comes to keyboards and especially mice it depends on the preferences of each individual.
Now for Windows you can get a "not so legit copy" if you understand what I mean. I'm not saying you should, I'm just saying you can.
Now here is the truth the components I selected are more than enough to play the games you listed. Actually it's overkill. I could probably select components than will cost about 550-650$ than will run the those games no problem. But there is a reason I decided go for what I did. First of all you gave me a good budget and secondly and most importantly I want to make sure that in the future when you want to play whatever game you want, you will have the power to run it even if that game demands a lot from the system. Maybe later on you want to play BF 5 (for example) and I want to make sure that you can.
Hope this helps and if you have more questions or didn't understand something feel free to ask.