Thanks for the ask, anon!
Favorite thing about them
I love her stubbornness. I think it is a really admirable quality, especially considering how much shit she gets and it would be really easy for her to just give way. But she doesn't and always stands by her principles.
Least favourite thing about them
I still love this about her, but it is probably her worst quality, and that is she is HUGELY judgemental in the early books, and comes to conclusions which she sticks by that are probably only reflective of a few little facts she has (like what she thinks of Jaime, and what she thinks of Renly).
"Lady Catelyn, you are wrong." Brienne regarded her with eyes as blue as her armour. "Winter will never come for the likes of us. Should we die in battle, they will surely sing of us, and it's always summer in the songs. In the songs all knights are gallant, all maids are beautiful, and the sun is always shining." (ACOK, Catelyn II)
I love Brienne and Catelyn's relationship in ACOK, and the sheer angst of Brienne being confronted by Catelyn's zombie breaks my heart.
This little couple called Jaime Lannister and Brienne of Tarth.
Some people seriously think that Hyle Hunt is Brienne's main love interest in the story so, although I really enjoy him as a character, I would have to say Hyle/Brienne.
If Jaime and Brienne were to get married, Brienne would spend the first few months thinking that Jaime is eventually going to get a mistress, because that is really common in the Seven Kingdoms. However, it never happens, and it just makes her love Jaime more.
idk if this is unpopular, but I've definitely seen some push back on this one. Brienne is super-unconfident about everything other than her fighting skills and her morals, and has a touch of social anxiety. That she is terrified of touching Catelyn and hides at the corner of parties is my main piece of evidence for this.
Song I associate with them
Either My Skin by Natalie Merchant, or Annie's Song by John Denver.
Favourite picture of them
This masterpiece made me cry for about a week after I first saw it.