A GTX 1060 6GB or an RX 580 8GB exceed the recommended specs of the games you've listed, so that's the min. you should look for on a PC if you want it to last a few years.
As for the CPU, it depends on what else are you going to do with it, but a fast quad core from Intel (I'd point to an i5-6500/7500 as the least you should get) will be enough. Ryzen is a good alternative, but only if you're going to overclock or you find a store that sells PCs with overclocked parts. If you find one, an R5 1600X should be the sweet spot.
Beyond that, the absolute minimum of RAM you need is 8GB, but you should really try to get 16GB.
You shouldn't have major problems finding a PC with all that for less than $1,000. Heck, if I can find a PC with all that plus a 120GB SSD here in Spain for less than 1,000 € WITH taxes, you should be able to find it for a lot less.
Please excuse my bad English.
Former gaming PC: i5-4670k@stock (for now), 16Gb RAM 1600 MHz and a GTX 1070
Current gaming PC: R5-7600, 32GB RAM 6000MT/s (CL30) and a RX 9060XT 16GB
Steam / Live / NNID : jonxiquet Add me if you want, but I'm a single player gamer.
