I do consider Finnceline to be the best AT ship but in the end I don't think it's worth it for either character.
Marceline would always be aware that Finn is going to die and be scared of that happening, and if Finn ever realized that too he would feel really guilty for doing that to Marceline. They would have great times but Finn would croak and Marceline would end off worse than she started.
She could turn him, but that's pretty cliche and boring and I'm not sure either character would agree to it. Marceline seems to have something against turning people (probably because she doesn't want more vampires around after killing them off and she also doesn't want people to live forever seeing everything die on them) and Finn enjoys being a human and growing up and I'm not sure I can see him going to it either.
It can only end badly, and that may be part of why I like it.