Given your budget(which is on the lean side), I would look at off-lease machines like the HP z620(check eBay). Those can be had with 6 or 8 cores, but you want to skip those that have speeds under 3GHz. Those machines are built like tanks. You also might consider a new Mac Mini M1 with 16GB of RAM. Based on reports, these machines perform way above their modest price.(and this advice is from a PC guy
). Another plus for the Mac is Soundflow (something that Windows users can't get as of now).
You mention that you have a more powerful machine for mixing, so why not do it all on that(why 2 machines)? And, note that sessions will move between Windows and Mac without any issues to speak of. Either install Mediafour MacDrive on the PC and keep sessions on an external drive formatted for Mac, or use dropbox(or any file sharing utility) to move sessions back and forth. Using WinRar on my PC, I have moved dozens of sessions between platforms for several years.
Here's an example of the HP I suggested with dual 3GHz XEON's, 32GB RAM, nVidia Quadro graphics and a 1TB SSD(add your own recording/samples drives) for under $600US(not sure about shipping):
https://www.ebay.com/itm/18529080223...Bk9SR76AwJjlYA
Probably add a USB3 card for additional ports