I am a chronic re-starter/character builder but often don't play deep enough to see how different builds interact with the story.  I have completed once on Veteran with a devoted fighter (2-hand)/beserker (no sub) build.  I am not a min/max, looking for the story while also enjoying the carnage.  So to my question - are there builds that interact better or in more interesting ways with the storyline?

 

Aumaua: island sub race + deadfire background gets a lot of unique conversation choices with the locals

Some of the priests get some interesting conversation choices

I've heard cyphers get some... but I haven't done a MC cipher myself yet so IDK how much so.

There is this spreadsheet that shows both responses and dialogue option count before the DLC 2.0, which pretty much backs up what Theosupus stated.  https://docs.google.com/spreadsheets/d/1VOXnwhAVZ2bqGJgw-cgJlG0TIqt9j3zJJbRx1epH3ho/edit#gid=0   

 

Picking out the obvious background/race/class tailored for certain story areas where it is totally relevant to your character such as Magran priest/FIre Godlike in Ashen Maw will usually let you get those unique bits though there are some like Rangers where the NPC just has to remark about your pet in the flow of conversation.  

 

In my personal experience,  I've seen quite a few of the paladins, priests, and cipher choices actively pop up while doing quests normally where many of the others are usually reactions.  Also, having a caster with a decent range of spell types does bring in a variety of ways to resolve map events.