An i3 with the a 1060/1070 , i have never heard of this . i think i3 will be a bottleneck for this setup
I think you confused on what a bottleneck really is. The bottleneck is simply the weakest link of a system. Every system, even the most high end rigs, has a bottleneck. Sometimes, the bottleneck can change between different hardware on the same system pending the application.
Look at gaming for example, the i3 8100 would push even a 1080ti in games that are not CPU heavy (even more so at higher resolution). Whereas in CPU heavy games such as BF1, the i3 will hold back even a 1060. So the bottleneck, or weakest link, will change depending on what game you are playing.
So saying "an i3 will bottleneck this setup" is both right and wrong. My advice is to decide which GPU you want, and then get the best CPU your budget will allow from there. In my opinion, you should build your system around the GPU.
GPUs tend to show their age much quicker than a CPU. For example, Sandy Bridge CPUs were released in 2011 and there are still a lot of them in gaming rigs today. The 2700k is still a capable CPU for gaming. Nvidia released the Fermi refresh cards in 2011 around the same time the Sandy Bridge CPUs were released. Nvidia just ended driver support for those Fermi cards. Basically, they are as extinct as the dinosaurs yet Sandy Bridge is still kicking.
In my opinion, a good balanced gaming rig would be to pair a 8400 with a 1060 (or 580 as the prices have dropped). This will allow you to game at 1080p at high settings in AAA games. For a budget system, I would pair a 8100 with a 1050ti. If you paired a 8400 with a 1050ti, it would run better in games that were CPU heavy, but there would be little to no difference in games that would not.
In short, I would not pair a midrange CPU with a budget GPU. It will work better in CPU heavy titles, but you will have diminishing returns in titles that lean harder on the GPU.