As you all know i ship FinnXFP so you know that Flame Princess is the one i would pick... but i have reasoning behind my pick besides the obvious "i want them to be together." or "they're so cute as a couple." reasons that everybody uses.
i will back up my claim with reasoning and discredit the other choices with reasoning. first i will discredit.

Bubblegum: now most people like to use the "she's too old for him" reason but that's not a very good reason because when finn turns 18 then age is no longer the issue. Finn is either 14 or 15 now and it's only a few short years before he catches up to her physical age. (Note~ bubblegum only ages if her biomass changes.) so age is not a good reason. no the reason i want to use is the fact that Bubblegum is prejudice and stuck up. she has shown to be inconsiderate time and time again. she puts science before everything including her friends and her kingdom. she has shown to be cruel uncaring in a few episodes. she is quick to judge without evidence or reason. and she has set finn aside as a knight or something expecting him to be there whenever she needs him without any sort of payment or reward for his help. she obviously notice his advances but just did things to leave him confused and hurt.
in conclusion she's a inconsiderate, stuck up princess who puts science before everyone and thinks she knows everything, she's judgmental and uncaring of those that aren't in her inner circle, and left poor confused finn heartbroken. Bubblegum doesn't deserve finns heart.

Marceline: well it's better than bubblegum but not by much. she has shown to have some compatible traits with finn, such as being outgoing and adventurous, she loves pranks and is really into messing with people. as quoted by finn "she's a radical dame who likes to play games." once again i would like to point out that the "age" reason isn't a good reason why they shouldn't be together. a small reason that i don't think she is the one... she's a demon spawn with a evil father. my main reason is that finn has shown no interest in going any farther in the relationship. he is perfectly happy with her being just his friend. and although it is shown in Bad Little Boy that maybe she has a crush on him and might be waiting for him to get older but i doubt it. she is more or less treating all of this as a joke. she mainly just likes messing with finn due to his gullibility that stems from his big trusting heart. then there is the "she's gonna have to watch him die" reason, which is crap. if she was serious about being with finn and wanted to be with him (which like i said is doubtful) then she could turn him into a vampire. now here's my problem with that, and no it's not the "he's gonna have to watch all of his friends die" thing, although finn and jake thought they wanted to be vampires in Heat Signature (only cause they didn't want to sit on the uncomfortable sofa) as finn matures he's gonna realize all the issues with that, not only morality but also emotionally it's gonna be harmful. and for a guy who has enough emotional problems and is all about his morals this is gonna be a major problem. Marceline also has a lot of baggage... she's got a bunch of emotional problems brought on by Simon losing his, her dad's evilness, and transition to a vampire.
~opinionated Reason~ Marceline is a demon spawn punk vampire, who treats everything like a joke. she's part of a scourge that needs to be wiped out. nothing good ever comes from a vampire, nothing good ever comes from a demon, so therefore nothing good comes from Marceline. ~Simple
in conclusion Marceline is demon spawn with daddy issues, she has a lot of emotional baggage, and she is a vampire who looks at finn as a gullible kid who she can mess with... and that's it. Marceline doesn't deserve his heart.

Fionna: well she is much better than Bubblegum or Marceline but is still not the best choice. i am sick of the people who claim the reason that they wouldn't work is cause they are too alike. that is a crap reason. typically this would be a good reason but in this case it's not. you see it all depends on what there personality and traits... like if someones sexist, selfish, or evil then they would not be able to get along with there counterpart. finn and fionna have no conflicting traits, in fact them having the same traits would do nothing but good for there relationship. now some people like to use the "the relationship will lose it's spark cause of their similarities", well here's my retaliation, use your brains guy's. Finn and fionna both are active, both are self-sacrificing people, both love adventuring, and killing evil. now tell me how adventuring and killing evil would cause them to lose their spark. they would able to go adventuring without arguing or complaining. think about it finn and fionna would be able to "date" in there own way... by going on adventures,going though dungeons, and maybe just running around having fun. i'd also like to point out that this is the only relationship (besides FinnXFlame Princess) that doesn't have the "age" problem that people like to use -_- and think of how they would react to the fact that their no longer the last human "oh my glob!" and if you read anything from astigpinoy then you know of the all important "saving the human race from extinction." now some people like to use the "they're bother and sister" or "they're related" reasons, and i would like to point out that this is a retarded, the genes in finn and fionna could be similar, i will not deny that, but if finn's dad and mom (who we have not actually met, Note~ his parents in Finn The Human episode may not have been accurate in the normal series, cause of the big difference in personality and appearance of finn.) switched gender then there genes would change due to the fact that changing the Y Chromosome that controls gender effects ever other gene in the human body, same as the X Chromosome. (note XY genes=boy XX=girl) this would cause a whole bunch of different genes to be passed down to the child aka Fionna (that's probably why she is cute chubby while finn is lean, mean, killing machine XD) this would make their genes unable to be the same/identical. this is under the idea that she is living in some sort of parallel world/universe or something and exists through genetics, if she came from magic or some other insane thing (ice King) then she would not even be close to being considered as finns sister. but unfortunately there is the undeniable fact that fionna doesn't technically even exist so if you don't exist you can't really have someones heart now can you.
In conclusion fionna is finn's gender-bent counterpart who shares a love in adventuring and protecting all things good. Fionna does deserve his heart but doesn't exist (unproven) and isn't the best choice.

Finally! now it's time for me to back up my choice.
Flame Princess: she is the best choice for having finns heart. It doesn't hurt my cause any to mention that they are ALREADY DATING. she is passionate like finn says and although people like to call her evil (i'm not gonna say any names...^_*) the only evil thing she ever did was attack that one goblin kingdom but it really wasn't evil it was just her letting her confusion and anger out, we all do that (just happens that she is a fire elemental with insane power.) people like to sight Flame King when they declare that she is evil... but that's just stupid, he obviously doesn't know he daughter very well. i mean it's not like family matters to flame king he killed his brother to become king and tried to put out his niece and nephew. she has a small temper but it is easily calmed by finn ;). Finn and her are pretty great adventures and they both seem to like to kill evil stuff as shown in Vault of Bones. finn's obviously in love with her cause he's willing to get burned just to be with her. flame princess loves finn enough to overcome her anger and burning tendency to save him. another thing people like to add is that she is "unstable" well that might be true, but who knows what the future will bring. maybe she will grow out of it, like fire elemental puberty or something. and if not then finn will find a way, against all odds, and all opponents he will find a way. flame princess's fiery nature only complements finn righteousness when adventuring and all though people like to call it a delusion, they can't deny that A. they're dating, B. she saved finn and went against her fire elemental nature, and C. that they are the most probable couple out of all of them.
in conclusion Flame Princess is a passionate girl with a fiery spirit, who has a temper that can be calmed by finn, and is in love with finn. Flame Princess definitely deserves finn's heart... if she doesn't already have it. :D