In terms of price to performance purely, the $100 increase on the 7870 makes the 7850 better in term of this. But in my opinion, get the best card you can get.
One thing I doubt is the CPU+Motherboard, it's very old for this 7870/7850. But since you're upgrading the MB+CPU+RAM, you're good to go. I personally recommend you to buy all of these together.
This is a good P67
Motherboard, another alternative is This P67
motherboard if you can pay more.
For CPU This
come on man, the K one is just $10 more
For RAM This