I would say your obvious bet here is a Ryzen 7 2700x for around $270, Motherboard around $130 so there's $400, 32 gig of ram is a real plus for 4k video editing so $275 for that now you're at $675, 2x 1TB SSD's will run you around $270, so $945, video card with any real power will run you $500 so $1445, and we haven't even hit Windows, the power supply, or case yet...
The point to all this is, you can build a 4k video editing system, but all the parts I've listed here are pretty mid-range in terms of cost and performance. Haven't even looked at SERIOUS 4k editing hardware like Intel i9s and AMD Threadrippers and RTX 2080 video cards. So if you have a real low budget like what you're working with, just...buy the best you can I guess. You'll be doing a lot of waiting on a $1000 budget 4k video editing rig. And you'll probably be running Linux, depending on how serious you are about saying within that budget.