I was kind of torn about Finn's house, but surprisingly the reasons people said Finn for Slytherin made me lean him towards Gryffindor. I've read this whole thread, so I saw a lot of the responses. When you people put that he made himself out to be a 'big-shot' all I could think about was the bravado that Sirius Black and James Potter had, and even Ron Weasley (yup the cocky moments, lol) had. Finn is not the Harry and Hermione type Gryffindor. He strikes me kind of as the Ron Weasley type Gryfindor. He gets scared, and he doesn't want to be in certain types of situations (like when Ron leaves Harry's side in book 4 and even in book 7) but when push comes to shove he does come back and he is a brave fighter. He does want to save his friends, when he tells Rey the truth he asks her to come with him, and he goes back for her. He does typical reckless things like stealing a flying car, I mean a TIE-fighter. He also does battle against the people he was scared of confronting. If you subscribe to the belief that tr-8r is one of the two guys left from Finn's little squadron then you can even apply 'it takes a great deal of courage to go against your enemies, but a great deal more to go against your friends' like Neville. Oh! Another thing, just like Sirius Black he comes from a place where darkness is all they know, and the way they grow up, and just like Sirius, he rebels and leaves.
So I think his qualities mirror more Gryffindor characters we've seen, then it does Slytherin characters we've seen.