Leliana--Welcome back hun! For my Quizzy, she'll probably be a little wary of Leliana to start with. I'd like to think my character has heard tales of the ladies in Orlais, and how many of them are bards.
Cullen--I've never been a huge fan of his, but I'd like to see how he's been holding up. I know that his Order is in shambles right now, and I'm wondering how all of that is going to play out later.
Scribbles--<clears throat> MIGHT BE NICE IF WE HAD AT LEAST A NAME FIRST!
Dagna--She was awesome in Origins and I look forward to seeing her again.
Varric--I'm one of those poor saps that hold onto the tiny hope that Varric is a LI. Regardless of that status, he was my best bud to Hawke and he'll be my best bud to my Lady Cadash
Cole--My character is going to be wary at first, like she will be around all magic. As long as the kid knows which way to point his knife, she's okay by him. She would ask Solas to keep an eye on him though.
Cassandra--It took me a couple of completions of DA2 to warm up to her, but we'll probably mostly get along. I tend to be more chaotic good as opposed to upholding order, but I'll see how it plays out. For now, I'd say friend.
Vivienne--So far, I can't say I like her all that much. However, she's an interesting and complex character. I can't say how well my Quizzy is going to get along with her. Before I played Origins, I had heard about Morrigan and I thought I was going to just hate her. While she does make some decisions that I absolutely think are stupid, she's my Warden's closest friend. Vivienne reminds me a little (just a little Vivi fans) of Morrigan, so her personality could surprise me too.
Blackwall--Definitely a friend, and one of the type of characters I've been wanting in my party for a long long time. I've been excited to journey with a Grey Warden again. I got even more curious about him when I posted the song "God's Gonna Cut You Down," by Johnny Cash into his thread, and Sheryl Chee (after honoring me with a like) told me that song was on her playlist for the character! I call him John Blackwall now. Interestingly enough, I remember reading that Alistair was originally thought of as an "old grizzled dark-haired war vet," before they scrapped that concept. It seems like that concept came back and I can't wait to find out more.
Sera--I'm the OP of the Sera fan thread (started back in March,) so it stands to reason I'm a huge fan of this character. I've helped gush about her for pages, so I'll let that speak for itself. I think her and my Lady Cadash will get along famously, although I can't say the same for future Inquisitor's down the road.
Iron Bull--Finally, someone that I can learn more about the Qun from. He seems brash, unapologetic, boisterous and larger-than-life in so many ways. I'm grateful I have a window to the Qun, which I've been wanting for a long time. It'll also be nice to see it coming from a qunari that's used to a lot of the culture of the rest of Thedas. I may not want to "ride the bull," but I'll happy stand at his back covering him with my bow while he charges into battle.
Solas--Even with his reveal, he's a total mystery. For now, I'll say friends. Sorry if I don't have a lot more to add than that
Dorian--I am going to befriend you. I'm going to befriend you so hard. This is the third of the characters that I've been wanting to see. I've been wanting to meet a good aligned Tevinter mage for a long time. Here's my chance and he seems like a fantastic guy. Plus, he's the first male companion in my history of playing BW games that has made me decide to try a m/m relationship my second or third completion of DA:I. Well done DG, well done! 
Wow...it looks like only Vivienne might be a sort of rival, and even then it could be subject to change.