My advice would be to get a ryzen 1600 , overclock it as you feel confortable, and then look in ebay for good deals with GPUs. But be careful with the power consumption. Stay at 4GiB of ram if you are only using 1 or 2 cards. upgrade to 8GiB if using more. You dont need to invest on a high end motherboard, you can just use risers if you plan to buy lots of them.

Overall you could buy a decent system pretty cheap

40$ - power supply
200$ - CPU
30$ - case
40-50$ RAM
70$ Motherboard

Plus whatever you plan to invest on gpus.

Also you must keep in mind that this is no simple hashing, as you said, this is real science, and real science uses a lot of CPU even when computing with the GPU (depending on the project, primegrid barely uses any on the other hand) . As an example, with a task from collazt that cpu wouldnt be able to completely feed a GTX1080.

Another, sexy, powerefficient and quiet option would be to invest that money in getting some of these beauties https://www.96boards.org/product/mediatek-x20/ or a similar product , but you wouldnt be able to compute on as many projects. The good news is that very good cpu projects like TnGrid , Universe@home and Drugdiscovery are avaliable for linux on arm.