Hm. I don't want to limit my options/can easily imagine anything could be great but realistically it would be helpful to have at least some letters in common.
N is nice because we can talk endlessly about anything. Or at least the things Ns like to talk about I suppose. But it's not a must. I just want the peson to be interesting and respectful.
I would find the often touted Fe doms to actually be the hardest/ least favorable ones, tho. Nothing against them as people but.... very different needs.
Here's my experiences so far:
INFP - Very fond memories. My teenage self might've wound up a very different person without her influence. I remember us talking very easily/freely and a lot. She said she read my writing and wanted to meet me because of that.
ESFJ - Desintegrated fast, ended painfully for both, we might as well have been speaking different languages. For a different person, he would probably have been a great boyfriend, but he basically thought I was a freak and randomly accused me of cheating.
ISTP - Never got all that 'official' but that suited us just fine. I liked the secretness. Probably would have been considered fairly unusual. We met infrequently. Interesting. Accomodating. Also fond memories.
INTJ - clearing the paper work to get married r/n. Sometimes it's like we have the same thoughts, and one of us will say them out loud just as the other is pondering them, but in some respects we're also very different. He's kinda more impetuous/action-ish than me but not so much that I can't handle it and he likes that I'm creative, give good imput and don't mind him working a lot, or so he says.
I guess in the end it depends on what ach individual INTP wants out of the relationship & what the other person is like.