Story wise I like being a human mage in DA:I. You are very invested in all of the aspects of the story. I do feel that multiple playthroughs are necessary to fully explore the story though. Some of the discussions I ended up in while playing a qunari mage were very interesting.
As far picking a race/class for an enjoyable powerful playthrough I would say that depends. I am naturally biased toward mages in all games. My first attempt was an elven mage but I couldn't continue as him as he looked too young and immature given my graphics level (sub-ultra on PC). I switched to a male human mage with a beard. I have made an Archer and a Dagger Rogue as well and a few more Mages of various combinations.
I like Knight-Enchanter Mage and Dagger Rogue best for opening up in a fight. I don't have to get too involved. But my Rift Mage is amazing and great. I find that building out the entire team and planning how the skills synergize really makes a difference. Spend some time on your tank and design that build to help the team. Look at combo's and how they play out For my mages I now include Cole and Cassandra in teams since I can give Cole knockout bomb and Cassandra has Wrath of Heaven. The sleep and stun synergize very well with Eldritch detonators. Both result in bonus spirit damage with high damage modifiers
Stun + Eldritch Detonator = Rupture -> 1200% Spirit damage and Weakness
Sleep + Eldritch Detonator = Nightmare -> 800% Spirit Damage and Panic
Personally I am not a good warrior player in any game. So I avoid them until I am nearly done with a game. But I do like DA:I's warriors. The specs are interesting. I hate the idea that warriors are natural leaders and reject that as truth. All of those concussions have cumulative effects right :-). I do like the idea that my dwarf ex-carta rogue is the leader of the inquisition. Hilarious anti-hero drama results.
All in all I don't think there is a best. I believe the best is what appeals to the player behind the console/keyboard. Enjoy yourself, everything is playable and works.