Would a 600w PSU be enough to power this build and what PSU would you recommend?
it should be enough
it is* enough ^
That is enough power. But you should use 1 (ONE) video card than two low entry cards. You can get a XFX Radeon HD 7870 XT 2GB Video Card from Aria for 143, its 3 tiers higher and cheeper than the two 7790 in crossfire with more performance.