$2,000 would result in an absolutely baller setup with a g-sync monitor and a videocard(s?) and CPU combo that would almost certainly be overkill.
$1,000 can still get you a really good setup, but the worse part is that you would probably lose the g-sync monitor (although you would still get a really nice one, just not with variable refresh rate). Frankly, you could put together a PC that will run all of that more than well enough (just maybe not at 4k x 120fps) for $600 or so.
Hell, even the mini PCs are getting pretty powerful now. I bought an Intel NUC a while back to replace my dying HTPC and I've gotten plenty of games to run at roughly the same graphical level as a Xbox 360. Yeah, that's old tech, but this thing is about the size of a cigar box.
Personally, I'm waiting until the 16nm GPU cards start shipping this year... I've been running a i5-2500K for about five years now and I've had zero reason to swap it out. The GPU is a bit on the weak side, but I don't want to lay out the money for a GTX 970 right now... that and frankly, if you're willing to adjust settings downward a bit, you can get a ton of mileage out of even middling hardware.