If you have $1600 for a new gaming rig, you will have no problems building a PC that will play any game on the market. I assume you are asking about a desktop PC and not a laptop. If I were you I would go to
www.newegg.com and buy your parts separately. But before that, you can go to
https://pcpartpicker.com/
I haven't used it in awhile but pcpartspicker is a really good site that will let you plan ahead and build your PC piece by piece while checking for compatibility issues and prices. When it comes to games, the CPU and GPU are the most important. But it's also important not to skimp on your motherboard. Get a good CPU for games from PDS and GPU for high end graphic intensive games like new first person shooters and the like.
I would recommend getting an AMD for your GPU. I actually prefer nVidia but their cards aren't doing nearly as well with the new Directx 12 as AMD is. So AMD might be the way to go in the future if your running Windows 10. If you go with nVidia, keep in mind the second number is more important than the first. As in the GTX 950 and GTX 780 are in about the same performance bracket. The budget 950 is newer but the 780 was a higher end card when it first hit the market years ago. You mostly get what you pay for with video cards.
When it comes to your processor, AMD CPU's usually have better performance per dollar while Intel is more expensive but offers higher speeds and usually better quality IMO. Like JakeCourtney said, you can't go wrong with a good i7.
Bottom line is for PDS games you really need to get a good CPU.
Also get you a good SSD drive for your OS.
