I want to see someone who is completely fine and happy, besides the current events. Someone who has a good life and no trauma.
Yes. I mean, some challenges and ambitions in life, sure, but I'm not a fan of tragic backstories and emotional drama.
Other than that... I think a gnoll companion would be cool. An intellectual type.
I'd love some evil characters that are either magnificent bastards or "fun" evil (...and not Astarion). Maybe crazy evil (like Xzar).
A vicious halfling in the vein of Montaron.
While I'm bringing BG1 companions as examples: a Branwen-like war cleric would be awesome. I initially thought I'd dislike Branwen (mostly the portrait, I guess), but I grew to really like her and kept her for the rest of my playthrough.
A classic dwarf. I usually prefer "weird" characters, but I like classic, stereotypical dwarf companions. On the topic of dwarves, a Varric-like companion would be great.
And of course a spiritual successor to Jan. That's a must.