If it were me, id suggest;
CPU; A Ryzen series cpu, probably ryzen 5 if you're trying to save money
GPU; a gtx 970+ a 1060 would probably fit within your budget
Mobo: really whatever is compatable with amd cpu and a gtx gpu +preferably ddr4 ram compatability, no less than ddr3
ram; at least 8gb ddr3, preferably ddr4 and whatever is compatable with your mobo
psu; at least 550, preferably at least 650, mines 750 because I like to future proof a bit
126gb ssd; good for loading windows onto to make your boot faster
1tb hdd; id say go for 2tb but hey, whatever fits your budget.
aftermarket cpu coolers are always nice, but not always needed, there are some pretty good/cheap ones on amazon such as cooler master hyper 212 and so on, but if it goes over your budget, just use the stock fan that comes with whatever cpu you get.
case; whatever suits your fancy, just make sure your mobo will fit into it, this is really only an issue if you get a regular atx sized mobo and a micro atx tower. also towers with optional fan slots are a plus, it gives you the option to add more cooling to the inside of your case.
I didnt list specific names nor prices on these, as it is pretty easy to google the specifications I listed to see what might best suit you, I think I covered everything but its late and im tired haha, good luck with your build let me know if you have more questions!