I would not hesitate to team a GTX 1070 with an i5-7400. However, if you have not yet purchased your CPU, I'd suggest stretching your budget to the i5-7500.
You can do better than that i5. Also a 1070 ( along with other high cards) is seriously overpriced. Anything over $410 is consider too damn much.
I paid 355 gbp for the gpu, i think it was a good deal. It's a Palit Jestream
I know the exchange rate is different, but that's still a pretty good price. If you already have the 7400 it works, but see if you can get the 7600 or even the i7 for those extra threads.
Depends how you use it. 1080p 144Hz then yes cpu heavy games will bottleneck, this is where i7's show their benefits. However 1440p 60Hz you will be fine.