You'll want a good GPU to train deep neural nets, and most libraries require one with CUDA support, i.e. an NVIDIA card.
The GTX 10 series essentially dropped the distinction between desktop and mobile cards, so you won't be giving up as much peak performance as in the past by getting a laptop. I still prefer to do such things on a desktop system with plenty of power and cooling headroom, where running at full tilts for hours or days on end is not a problem. Doing the same on a laptop feels like asking for trouble.