The power supply will work for two Radeon HD7850's, I would also get a Samsung 830 ssd for you operating system and antivirus, and a regular sata hard drive for your games. When you load your system leave the sata hard drive disconnected until the operating system is installed.
I would not crossfire with a pair of lesser cards, I would go for a single powerful card like a 7970/7950 or a GTX660Ti/670. Any stuttering issues are compounded by dual cards and there are games which actually run worse with dual cards.
Aside from that, I would be looking for a 700W+ supply for crossfire. Your 600W supply is more than ample for a high-end single card.
A Corsair TX 750 V.2 isn't a bad option, but in terms of just everything; heat,power,room I would go for a single card because those cards roughly together are about 400-440 depending on the manufacturer with that I would get a more powerful card like a 670,680 or 7970, 7950 It will do you much better.