Can I do deep learning with the 1060 or the 1070 ti? Before I start, I want to let you know that I am completely new to the field of deep learning! Since I need a new graphics card either way (gaming you know) I am thinking about buying the GTX 1060 with 6GB or the 1070 ti with 8GB. Because I am not rich, basically I am a pretty poor student ;), I don't want to waste my money. I don't need deep learning for my studies I just want to dive into this topic because of personal interest. What I want to say is that I can wait a little bit longer and don't need the results as quickly as possible.

Can I do deep learning with the 1060 (6GB seem to be very limiting, according to some websites) or the 1070 ti? Is the 1070 ti overkill for a personal hobby deep learner?

Or should I wait for the new generation Nvidia graphics card?
Regarding specific choices I can't recommend, but if you are completely new, you should probably learn/code some more until you get a GPU. There is a lot to learn in machine learning before GPU speedups make a significant difference, and until then doing the computations on any old CPU would be just fine, especially if you are just starting since you won't be doing anything too complex. You will know when computational resources are your main bottleneck, and until then it shouldn't really matter too much. 

Or, you could also rent computing power from say, AWS or Google