How Much Watts Will I Need To Power This System?

If you're looking for top quality, the 80+ Gold Seasonic G360 is your best choice. A little lower, get one of the 300W-350W 80+ bronze Seasonic units.
These recommendations are based on no future graphics card upgrades to anything more powerful than a HD7750. If you will ultimately play games on this system, and plan on adding a more powerful graphics card, then you'd probably want a PSU closer to 500W even though you won't need that much power now.