I wouldn't go all the way down to H110.
Both H170 and Z170 have a PCIe x16 link between the primary PCIe connector and the CPU, so that's not a deciding factor. However, Z170 allows for 20 additional lanes while H170 only allows for 16. However, that mean that both could support three-way SLI or Crossfire with all cards running at x16. With H170 could have three way SLI or Crossfire with the third card running at x8 and then have a sound card and USB/Firewire/Ethernet card as well. With Z170, you could have three way SLI or Crossfire with all three cards running at x16 and then have sound card and USB/Firewire/Ethernet card as well.
I would go with H170. It seems better for your budget, since I doubt you're going for extreme SLI or Crossfire when you're looking at a non-K SKU CPU.
As for the CPU... I recommend the Intel i5 6500. It offers a much better price/performance ratio than the i5 6600.
Here are all ATX boards with the Intel H170 chipset and FCLGA1151 socket.
Here are all mATX boards with the Intel H170 chipset and FCLGA1151 socket.
Here are all Mini ITX boards with the Intel H170 chipset and FCLGA1151 socket.