No, processor won't fit in the motherboard. You'll need either an 1150 mobo or an 1155 cpu. You might want to get a power supply with more watts too. It would probably work but it'd be cutting it close. Also I always prefer power supplies to be gold certified and I usually go for Seasonic ones.
You could stick with the board you had and you could get an i5 3570k which is an 1155 part. Or you could get the Z77 Extreme4 by Asrock if you're willing to spend some extra cash.
Still think you need to beef up that power supply too,
The two main power draws in a PC are the graphics card and the CPU. If you look in the specs of your specific choices you'll see how many watts it takes to run them. I typically like a buffer for other power draws like HD's, fans ram etc. Also if you overclock anything they will draw more power. So overclocking overhead needs to be addressed as well.
The 280x is 250w and the 3570k would be 95w stock. Thats already 345 watts not taking into account everything else. Less than 100 watts isn't much overhead. i'd suggest at least 500 watts although a 550w power supply thats gold rated should be cheap and easy enough to find.
You would probably be fine if you went to a lower speed on your ram (I'm currently using 1600mhz with my 8320) largely because the higher speeds are more helpful/ effective if you are using something like an apu (correct me if I'm wrong). If I were you I would personally go for a larger hdd so you don't have to worry about running out of space as quickly, but that's just my opinion.
This is best gaming CPU and IMO best motherboard and the sweet spot of 1866Mhz CL9 1.5v for ram .... and SSD for boot drive and 1TB hard drive for storage R9 280x GPU and 600w PSU