FSP makes some good power supplies, but that isn't one of them. That is a fairly low quality or at best, veeeery mediocre unit. I would definitely not recommend using it with anything more capable than your current GTX 960, and probably, I would not have ever recommended using it with anything more than maybe a GTX 750, 950, 1050, etc.
This is probably about the best you could do for that price. And for reference, you'd probably be able to high to very high (Or in some games, ultra) settings at 1080p, with an average of about 30fps higher than on your GTX 960. Probably more than that on some titles.
If you can swing a few extra bucks, this would be a pretty dramatic increase in performance over what you have now. Don't let the "2.9 Ghz" of the 9400F fool you. That CPU has a max boost of 4.1Ghz and "lives" around 3.9Ghz when all cores are under full load boost conditions. It is VERY capable for a 144 dollar processor. Also, the CX PSU listed below, while not a top of the line model, is miles better than your current FSP unit.
PCPartPicker Part List
CPU: Intel Core i5-9400F 2.9 GHz 6-Core Processor ($144.89 @ OutletPC)
Motherboard: ASRock B365M Pro4 Micro ATX LGA1151 Motherboard ($74.89 @ OutletPC)
Video Card: MSI Radeon RX 570 8 GB ARMOR OC Video Card ($144.99 @ Newegg)
Power Supply: Corsair CX (2017) 550 W 80+ Bronze Certified ATX Power Supply ($64.98 @ Amazon)
Total: $429.75
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-10-28 21:21 EDT-0400