Recommended PSU for my Case/Setup under $75

Supplice VI

Honorable
Feb 12, 2014
5
0
10,510
After asking previously about my build and its compatibility with certain graphics cards (As of which I have decided on a Sapphire R9 270x Toxic (or Vapor-X, still have to measure for space)) I realized I need a PSU. The graphics cards weren't exactly hard to understand in terms of what they need, where they can fit, what cables go where, and so on. The Power Supply, however, is a problem.

My current (Stock) setup

Internal view

The card that's making me ask this question

Now here are the problems at hand:

I have no idea what an ATX-internal form factor is (or moreover, how/if it differs from regular ATX)
I have no idea if any of the power supplies can even fit (which it looks like most of the cannot)
I know I need 500w minimum, but I'm looking for 600w-700w as a precautionary step in computer longevity.

Some recommendations are requested on what my next move is. Do I have to buy a different case for the PSU? What PSU should I get?

TL;DR:

PSU that fits 150mm x 140mm x 86mm (5.9 x 5.5 x 3.4 inches) (Unless it doesn't matter)

600w-700w

For under $80

If there is no PSU that fits, what kind of case should I look at?