Graphics card info needed

I am currently building a computer but I have one question.

Using the video card XFX Radeon R9 280X 3GB DD what type of CPU would I need? 

I keep reading that I need 750 watts but I am not fully sure. I am extremely new to pc building and really need the help.

You would need 750w (perhaps 800-850) if you wanted to use two of them. A good 550-650w power supply would be plenty for a single 280x.

As for CPU, I would most likely recommend an i5 4690k or FX 8350.

How would this build work?

(I have 600 watt, I just am buying it from somewhere else)

Make sure the 12V rail on the PSU has enough amps on it. Amperage is more important than wattage. Some PSUs may be 650W but the power is over many 12V rails and each is relatively weak, only 20 or so amps, and it won't work. The EVGA B something PSU is guilty of that. They claim it can run two GPUs. Most of the time it can't run one. 

Agreed. The 4690k is good as is the 8350. On the cheaper side take a look at the FX 6300. Also the Xeon 1230V3 if you don't want to overclock. 

A good 550W PSU (re. Seasonic, Corsair, Enermax, Silverstone) is plenty, but I'd go 600-650 for a little more headroom and longevity.