I built a system for a friend with a R9 280X and an FX-8350 and it hasn't had any problems with a Rosewill Hive 550W. It's $70 right now on Newegg which is above your budget, however generally any 550W unit from a decent company would be good. This is a good reference: https://community.newegg.com/eggxpert/computer_hardware/f/135081/t/45344.aspx
The 285 would use even less power than the 280X, and the 960 would use even less than that. Switching to the Intel 4440 would again lower the power requirements even further for all three of the GPUs.
I'd personally go with these which should be able to handle any of those configurations:
Corsair VS Series VS550M 550w PSU
SeaSonic ECO 600W PSU