It's a 265W one in that Optiplex so it's cutting it close with the 1060, but it has a 6 pin plug and more importantly it's got ATX mounting holes so it can be replaced if you really want to down the road. Some of the small desktop and SFF Dell units can be a bit of a pain to work on, but the mini tower's really aren't that bad at all.
Another fun option would be to buy a used T3500. They go super cheap used these days (I see them locally at resellers with a dual core and 8GB ram for CAD$150), and you could toss in a CAD$100 six core X5670 (edit: or W3670). Those have a 525W supply and a bulletproof chassis. That platform's getting a little long in the tooth, but for <$250 it's a hell of a value given how rock solid those Dell workstation cases are.
Edit: And the $250 T3500 conversion with the Xeon version of the i7-970 is still as fast or faster that an FX8350 unless you really overclock the FX-8350.
http://www.anandtech.com/bench/product/157?vs=697