As said before, the i7 3820 and the Z87 platform are not compatible. For the i7 3820, you would need an X79 chipset. If you want to keep the Z87, I suggest going for an i5 4670k, or an i7 4770k if you need the hyper threading.
Unless you're getting the GTX 670 really cheap, I would suggest going for a 760 or 770, or wait for the upcoming AMD R series which is coming out next month.
PSU wise, 750W would be safe for a multi-GPU configuration without needing to upgrade again. If you have no plan to go multi-GPU, you would get away with a 600W PSU. I recommend really anything, other than the CX series, from Corsair, or Antec/Enermax/Silverstone/Seasonic/XFX.
Optical drives shouldn't be too much of an issue, you can get a decent one for $20.
Ram wise, save some money and go with two 4 GB sticks. Unless you're doing professional editing (In which I would go with the i7 4770k as a pairup), you don't really need 16 gigs, and would probably never even get close to using it.