Well for $600 (assuming you don't buy an OS) you are going to have a pretty weak gaming PC, I would get the PS4, you will have a great gaming experience for the next 6 years and you don't have to put any money into it other than games. A $600 PC will need a better video card in a year or two.
You should definitely get a PC! Most games aren't $60 each! Mice and keyboards are WAY cheaper than controllers. A $600 PC will get you High-Ultra settings on most games. PC for sure! PS4 isn't bad either. But you have to pay to play online.