Another option is to look for sales on pre-built machines (DELL, Best Buy, Staples, etc.) and add a used GPU. I recently bought a GTX 950 card for $100 off kijiji.
https://www.dellrefurbished.ca/ offers desktop machines that are returned from lease. And if you subscribe to their emails they frequently have coupon days where you can get an additional 30 or 40% off. They are typically Windows 7 machines, but you mentioned you have an OS.
Lastly, save a few more bucks and go for $700 machine. That'd make a big difference. And the $700 could go even further if you wait for back-to-school sales or black friday.