Here's the optimal path through the Dwarves chapter, divided in two parts:
Part 1: Advanced Scouts -> Dwarven Portal and Portal Tracks (order irrelevant) -> Granite Mine -> upgrade all to level 2 while researching Dwarven Residences -> Planks, Marble and Steel (order irrelevant) -> Copper Foundry -> begin upgrading Granite Mines and Portal to level 4. This should take priority over unlocking techs.
This leaves you with the following techs that do not require Dwarven resources: City Expansion 21, Squad Size Upgrade 16 -> City Expansion 22, City Expansion 23 (comes after Granite Mine but does not require Granite). All of them are not essensial and can be left for later, so best to work on them while upgrading your mines.
Part 2:
- Dwarven Workshop -> Dwarven Barracks. If you don't have enough Granite for Barracks - work on one of the above techs
- After that Sword Dancer/Axe Barbarian Promotion and Ancient Grounds (order depends on which one you need more) -> Dwarven Main Hall
- next you can work on three techs that all require Copper but no Granite. If you are low on Copper - work on one of the above techs or on Squad size Upgrade 17, else work on one of those techs while waiting for Granite
- next Dwarven Style Street and Dwarven Style Armory (again the order depends on your preferences and what you need) and following techs
- Dwarven Ancient Wonders
There are three spots where you can get stuck if you don't have enough Granite Mines and Copper Foundries, or if you get too many KPs from tournaments: "Tavern and Temple", "Golem/Paladin Promotion" and "Dwarven Ancient Wonders" (in other words the three most expensive techs). I have finished the Dwarves chapter in both worlds following the above path through the tech tree and I got stuck on the AW tech because of getting too many KPs from tournaments, but that's the only place where I got stuck for more than a few hours.