You will need to wire up both connectors but can use a daisy chained (dual 6+2pin) cable on a single GPU. It's only a concern for extremely power hungry GPU's that may require two completely separate cables.
Not exactly a budget... The Corsair CX450M and the Seasonic S12II 520 are both good options. The former is "better".
If I may, I have a few other suggestions for your build:
-Scrap the cooler (use the stock one) and lower the motherboard to a H170 or B150. You're not overclocking. Save the money and put it towards a SSD. Preferably a 120GB one at the very least.
-Get the RX 480 4GB instead of the GTX 1060 3GB. More VRAM and a better card overall.
-If you're going ahead with the i5 7500 and a H170/B150 mobo, you may need a BIOS update. It'd be best if you got a B250/H270 motherboard or a i5 6500 instead.