Is this a good $600 budget build?

Not that motherboard . MSI boards did not have overheating protection for the voltage regulators till the G46 model . They can burn out .

Spend a little more and get this model from Gigabyte
http://pcpartpicker.com/part/gigabyte-motherboard-ga970ads3p
Or better still the ASUS M5A97 R2.0 [ which costs another $10 ]

You can cut the RAM to 2 x2 gig if you need to save some money . That will not make any difference to game performance
http://pcpartpicker.com/parts/memory/#v=1500&t=11&s=301600&z=4096

And definitely go with the 7870 .