The Solasmancing Female Elf is probably the one that gets the most meaningful extra content lore-wise out of their LI. However, any species pretty much works and I always take a special joy roleplaying those odd ones out who no one, them including, would expect to be there. As a dedicated Cadash player, it was also fun to be someone who really does not have that much of a stake in this whole thing and trying to imagine how they would approach the mage-templar war from a semi-outside perspective. Obviously the Lyrium trade is still dependant on the outcomes, the hole in the sky is worrying for everyone, and dwarves can still get conventionally attacked by demons, but that's about it.
Class-wise, I think it depends more on who you want to bring along (or who your Inquisitor would be friends with and would thus spend their time with). If you always want to bring Blackwall, you probably don't need a tank; if Varric's with you then maybe not a rogue because two rogues can get really unwieldy in higher difficulties since they cannot be left to the whims of the AI, etc.