yeah - grow your budget - i just finished a pc, about $3800 invested -
first decide on the software you'll be using and research if it's going to be a core hog
i do a lot of video rendering, and on my i7-4790 4 core cpu (which wasn't a dog, while rendering with one program, Handbrake, was running at 98-100% load on all 4 cores. On my new 8 core cpu, it runs at 92%-95% load on all 8 cores, but time to render dropped about 60-65%, from 45 minutes for one file to 17 minutes
decide the cpu you're going to need and go from there