How much power would my computer need?

Go to PCPartPicker and use it to plan your build. At the top it will show you the nominal power this will take. Then you find a power supply that is 2X this number because you want your power supply to be running about 50% of max capacity for normal use.

The thing that determines what PSU you need is the graphics card
In this case 350W minimum needed + 1x 6-pin Supplementary Power Connectors

I would strongly advise going better than this and get a quality branded 500W PSU such as Seasonic antec coolermaster or corsair branding

There's two sites you can go to to calculate your PSU requirements:

Pick Parts, Build Your PC, Compare and Share - PCPartPicker
http://pcpartpicker.com/

With this one, you can put your components into the site, and you will see a power rating for the overall setting near the top, as you build it.

eXtreme Power Supply Calculator
http://outervision.com/power-supply-calculator

This a simpler online calculator, and it doesn't concern itself so much with full details.

500 or 600 would be about right

RAM and Processor.

350W is the bare minimum, but you're gonna want something better than this. A 650 W PSU will do you fine, especially from a reputable brand like, EVGA, Cooler Master, or Corsair.

I always plan power supplies on the assumption of a maxed-out set of expansion slots, plus whatever additional +12VDC is needed for the planned video display adapter's GPU power regulator, in order to provide sufficient reserves for any contingency. Advanced Micro Devices® FX-Series™ Main Processing Units (Socket AM3b) draw 125maxW for eight cores (with the exception of the FX-9000 Series, which demand up to 225maxW plus refrigeration). The nVIDIA® GM207 can draw enough power to warrant a 6-pin PCIe auxiliary harness.

Antec having discontinued the TruePower Quattro series, and the HCG-900 being short two +12VDC rails for the revised EPS12V specification, I recommend the LEPA® G1000MB MaxGold™, which has a +3.3VDC/+5VDC combined capacity of 130 W and 20 A x 4 usable +12VDC capacity (incl. one rail for CPU power and one for GPU power).