"I'm afraid the CPU will bottleneck and it will make the fps lower than the 1060" This is not true.
At 1080p in certain games your I5 will limit the GTX 1070, however, the framerates will still be higher or equal to the framerates with the GTX 1060.
What resolution is your monitor? CPU and gpu usage and bottlenecks will depend on games played and monitor resolution.
Also, I would recommend a 1060 6gb if you do get a 1060. The 3gb vram on the 1060 is limiting.
The performance wouldn't be worse then the 1060 if you were to get the 1070. And as for the "bottleneck" it depends on the game and resolution. Either card would be fine for 1080P but the 1070 would be better for 1440P gaming.
Unless the pricing is stellar, for those cards, I would look at a 1660, or 1660ti, instead. Even if there is a bit of a bottleneck, you can always reuse the graphics card, once you upgrade the CPU. Also the faster GPU will last longer, with regards to how long till you need to upgrade again.