DISCLAIMER: I have not seen any of the nominees in the categories of Foreign Language Film, Documentary Feature, Documentary Short Subject, Animated Short, Live Action Short Film, so I have no view on them.
When it comes to the Oscars, one can pick what is likely to win, and what one would like to win (or, according to the more arrogant out there, what should win). On the first point, the easy answer is what has won so far. If a film has won awards at the Golden Globes and the BAFTAs, not to mention various critical awards and those of the various filmmaking guilds of America, it is likely to pick up Best Picture at the Oscars. This is not a hard and fast rule, but it is a tendency.
As previously mentioned, I predict that Three Billboards Outside Ebbing, Missouri will pick up Best Picture. What I would vote for, were I a member of the Academy of Motion Picture Arts and Sciences, is a different matter. Of the nine nominees, I was most impressed by Dunkirk, but World War II films are such clichéd Best Picture winners that I would not vote for it. In a year when focus is on gender relations in the film industry, I want to support a film that has something positive to say about women, and is also something outside the generic norm. Lady Bird and The Shape of Water fulfil those criteria, and the latter is also a fantasy film, extremely rare in these circles. Therefore, in my fantasy AMPAS vote, I would pick The Shape of Water.
Three Billboards Outside Ebbing, Missouri (predicted winner)
Three Billboards Outside Ebbing, Missouri is a surprising lead contender for Best Picture because Martin McDonagh is not nominated for Achievement in Directing. If he were, I would predict a victory, but as he is not, I have the same dilemma. Much as I love Christopher Nolan, he has opted for a safe award genre with his World War II thriller. As impressively directed as Dunkirk is, I want to see him garner awards for science fiction films like Inception and Interstellar. Therefore, I champion another of my favourite directors, Guillermo Del Toro. Handily, I suspect he will actually walk away with the award anyway, which will make me happy.
Paul Thomas Anderson, Phantom Thread
Guillermo Del Toro, The Shape of Water (predicted and preferred winner)
Greta Gerwig, Lady Bird
Christopher Nolan, Dunkirk
Jordan Peele, Get Out
I have not seen any of these, but I would be flabbergasted if Coco did not bring Pixar another award.
The Boss Baby, Tom McGrath, Ramsey Ann Naito
The Breadwinner, Nora Twomey, Anthony Leo
Coco, Lee Unkrich, Darla K. Anderson (predicted winner)
Ferdinand, Carlos Saldanha
Loving Vincent, Dorota Kobiela, Hugh Welchman, Sean Bobbitt, Ivan Mactaggart, Hugh Welchman