Never buy HP. I say that as someone who has everything HP. Build quality is junk, they’re just cheap. But the cheapness has drawbacks. No proper heat dissipation on laptops for example.
What you want is an i7 6700 HQ, 16GB RAM, and an Nvidia 960/970/980. Ideally you want also an M2 SSD for your OS and an additional 2.5" SATA slot for a HDD so you can pick up a 1/2/3/4TB drive to stick in there depending on your needs.
For brands I would advise Lenovo or Asus and really nothing else.
For size I personally think the benefits of having 17.3" over 15.6" are massive. That 1.7" difference just makes the working experience so much mor enjoyable. There is also the added benefit of increased productivity through a larger screen size. The drawback is size/weight for carrying it around.