Here are my guesses (FYI, I think that Cole will be the last rogue confirmed, and Scribbles is a Lucrosian mage, who values money and serves as an economic adviser)
Cassandra to...
Varric - They will get along, but have professional disagreements along the way. She's a pragmatist, he likes to help others
Vivienne - They both respect each others iron will
Iron Bull - She might get put off by his rowdiness, but they will understand each other
Solas - She will not trust him, because he knows a lot about the Fade, and that might make him suspicious
Dorian - She will respect, but not fully trust, him
Blackwall - She will respect his desire to leave the Wardens and do what is right for all, and relishes the Warden philosophy of do whatever must be done
Cole - He's a murderer who's killed Seekers and a spirit, so he can't fully be understood. She won't trust him
Sera - She is a thief and thinks only of small gain, so Cassandra will not care for her. Further, she will be off-put by her rowdiness
Cullen - She's an internal affairs agent for the Templars, and distrustful of what happened in Kinloch Hold and the Gallows. More to the point, Cullen believes in sparing people who may or may not be innocent. Cassandra prefers to not take risks. But she will help him with the military.
Scribbles - Cassandra will only value her for what she can bring. She doesn't think much of coin
Leliana - Professional rivalry, they accomplish their tasks in different ways, but they will respect each other.
Varric to...
Vivienne - Won't like her, she'd kill someone just for looking at her wrong. Too much like the Merchant's Guild. Nickname: She won't have one, he's too scared of her
Iron Bull - Varric doesn't trust qunari after the Kirkwall thing, and will only come around if Iron Bull abandons the Qun. Nickname: Horns
Solas - He'll be warm and welcoming, but tease him. Nickname: Professor
Blackwall - He'll try, and fail, to get him to lighten up. But Varric will be okay with that.
Dorian - Varric will get along with him just fine, seeing as how Dorian has no qualms calling out the bad people of his kingdom. Nickname: `Staches
Cole - After knowing what Anders did, he's not going to trust this guy. Nickname: Ghosty
Sera - They will drink together all night long! Nickname: Jens (since she's a friend of Red Jenny)
Cullen - He'll think highly of him since he stood against Meredith to help the innocent and not be a tyrant. He'll also encourage him to lighten up. Nickname: Captain Temples
Scribbles - He won't talk to her much, but he'll be more than happy to let her handle all of the economic problems he assigns to the family pets. Nickname: Coins
Leliana - He and her will get along very well, although he'll get annoyed if she talks about the Maker and the Chantry. Nickname: Eyes
Vivienne to...
Iron Bull - They'll respect each others talents as a way to get things done. But Iron Bull will be wary since she's a mage.
Solas - Won't trust him, since he lives outside of the Circle
Blackwall - Will trust he can defend her, and hopes he truly will do what it takes.
Dorian - She'll agree Tevinter has problems, but won't trust him, since he isn't the circle either.
Cole - She knows very well the dangers of spirits
Sera - She won't like her, she's a thief, she's incredibly petty, and submits to no one
Cullen - They'll talk for hours on the best ways mages and templars can work together to implement the Circle. But she'll think he's too soft
Scribbles - They will be the best of allies, if not friends.
Leliana - Will think she's soft and relies too much on subtlety, and use it only when she thinks it's the best option
Iron Bull to...
Solas - He knows better than to trust an unleashed Saarebas.
Blackwall - He'll know the stories of the Wardens, and respect them
Dorian - Not just a Saarebas, but a Tevinter Saarebas. They'll probably fight
Cole - Won't like him at all
Sera - They'll have fun together
Cullen - Will consider him pretty ineffective, not willing to go the full length
Scribbles - Will keep her at arm's length
Leliana - They'll tease together, but the relationship will not be a close one
Solas to...
Blackwall - Won't think too much about him one way or the other
Dorian - Will respect his power
Cole - As an expert on the Fade and it's denizens, he'll treat Cole differently, and with more understanding
Sera - She will tease him, he won't like it, she'll tease him more. Good fun by all
Cullen - He'll keep a wary eye on him, but will get along
Scribbles - They won't understand each other, but not hate each other
Leliana - They'll tell stories and understand each other