Friends:
Varric. Simply because he's Varric.
Alistair. He's a lot like me in some ways, and I just can't see myself not being friends with him.
Iron Bull. He's honest, funny, loyal, and a good friend. Definitely going to be friends with him.
Anders (Awakening). He's like Alistair, just more experienced with the world as a whole.
Fenris. Aside from his distrust of mages, I find myself getting along with him really well. I'd try to avoid topics involving mages for the most part, though.
Cole. He's like the little brother I never had.
Merrill. She's like the little sister I never had.
Isabela. She's basically a female pirate version of my dad, so I'll definitely get along with her.
Bethany. It'd actually be more than just friendship... 
Zevran. Similar reasons as with Isabela.
Oghren. He's hilarious!
Shale. Do I really need an explanation?
Dorian. He's awesome.
Dog. I'm a dog person, what can I say?
Aveline. While we may disagree on court-enforced justice vs. personally-enforced justice, I think we'd be pretty good friends for the most part.
Blackwall. idk why, I just think we'd be good friends. Probably because I'm pro-Warden.
Solas. I'm a big elf fan, so yeah.
Sigrun. I can relate to her in some ways and she's also pretty friendly and funny.
Justice (Awakening). I find myself agreeing with him a lot.
Nathaniel. He's a good friend, if a bit slow to trust.
Josephine. She's friendly, if a bit.... finicky.
Acquaintances:
Sten. I don't see myself becoming friends with him, but I would like talking with him from time to time.
Sera. While I think she's pretty funny, she just refuses to actually think, which is a real hang-up for me. Not friends, but not quite rivals either.
Wynne. She's kind of grandmotherly, but also fairly pro-Circle, which conflicts with my views on the Circle. On the whole, though, I think we'd get along, for the most part.
Morrigan. She's too 'ice queen' for me, but I think we'd get along most of the time. I can see myself messing with her from time to time just to get her annoyed, though.
Velanna. I'd actually just keep my distance from her, tbh.
Cassandra. Pretty sure that we wouldn't get to the friendship stage, but we'd probably get along.
Leliana. She's too girly for my tastes in DA:O, and she's too much on the cold and calculating side in DA:I for my tastes as well. Acquaintances at best.
Vivienne. While I disagree with her pro-Circle views, I like that her reasoning isn't just the usual 'mages are dangerous' BS. It'd be interesting talking with her, at least.
Seb. He's boring, so I wouldn't really talk to him much.
Cullen. He's pretty reasonable in DA:I, so I'd probably get along with him.
Rivals:
Anders (DA2). He's way too serious and depressing in DA2, not to mention that he nearly constantly bashes on Merrill, which really gets on my nerves. I'm sure that I would end up punching him at some point.
Carver. He's annoying and so damn focused on making a name for himself that he actually gets upset with you if you help him out. Wouldn't get along with him.
Loghain. If he ended up becoming a Warden, then I probably wouldn't get along with him. I mean, he was the main chaos of the civil war, and his obsession with Orlais is just... idk, ridiculous.
So, basically, I'd get along with pretty much everyone and only clash with a couple people.