Which race/class you prefer for the protagonist?

I have a number of factors that led to my choice. First off, I absolutely love dwarves. I also like variety and unique roles, builds, and equipment. I never play as a human if I have a choice, and I am not a real big elf fan, but I have a couple elf characters in other games already due to the elf or human race limitation. I am rather attached to the Dalish and elves in Dragon Age though. I find their history, faith, and culture interesting, so my desire to roleplay as one in the setting causes me to keep gravitating back to them. My warden was Dalish until I encountered some issues with Merrill dialogue in the sequel, but it helped me discover my true love of Aeducan. I also tried out a Dalish in Inquisition to make up for it, but there were numerous instances where the general dialogue sounded out of place; though, this may have been due to trying to get along with the Chantry-folk and not declaring Dalish glory. I desperately wanted to use a Qunari, but I had been putting off my Templar canon, and Inquisition might be my last chance. I prefer my warriors NOT to be from giant races. So, I wound up with this:

DAO-Female Aeducan stealthy archer rogue with traps, romancing Leliana
DA2-Male Hawke dual wield dagger rogue combo enabler, romancing Merrill
DAI-Male Cadash two-handed Templar warrior tank, romancing Josephine then Iron Bull

In hindsight, I wish I had taken advantage of Origins' freedom, and played either a two-handed or shield melee rogue. I also tried to make a mage Hawke a couple of times, but was defeated by the lack of immersion. Amusingly, the second time I even made loads of restrictions (no robes, staves had to look like polearms, funny personality to get people to ignore him, no magic spells or auras within city limits, etc.), but I still didn't feel right about it.

I also like variety within groups as well. I ultimately chose rogue for Hawke, because I loved how it spread the classes out amongst the siblings. Similarly, in Kingdoms of Amalur the two main npcs and occasional companions you interact with are a warrior and a rogue, so I played a mage.

To be honest, my Inquistor is still somewhat fluid. I could see switching to Qunari mage in Inquisition. On the other hand, since my ideal mage would be a Spirit Healer split between Creation and Entropy schools, I find Inquisition's spell selection rather atrocious. I have numerous other games that help inform some of choices. While I prefer shields, I already have awesome shield warriors in Dragon's Dogma, The Technomancer, and Diablo 3 (non-elemental, shield monk). My tank in Inquisition uses mostly Vanguard and Templar abilities, so two-handed was a great pick seeing as how I really only wanted Mighty Blow.

But my choices are also influenced by stories and characters. I hadn't played an Andrastian yet, so having an ostracized Carta negotiator get to embrace his faith in this manner was great. I especially love playing the faithful role from outside the human perspective. At one point, I had my Inquisitor finishing the romance path with Josephine. That story was fun to me because Leliana had become such good friends with Josephine, and they both ended up with dwarves as the love of their lives. Even if for only the briefest of moments, I imagine Leliana was a little jealous that Josie ended up with an Andrastian dwarf. The romance choice was eventually swapped due to my compulsion for variety though. My Shepard is a bisexual woman who went from Liara (even if I didn't like her as much until later) to Garrus, while my male Hawke was "elf-sexual," and completed his arc with Merrill. For my Inquisitor, I wanted his final pairing to appear less heteronormative from the outside. And while some people didn't care for the dominant nature of the romance, I felt like my Cadash did get exactly what he needed from the Iron Bull.

EDIT: What I mentioned above about swapping for Qunari in Inquisition would really only come to pass if Qunari were unavailable for race selection in the sequel.