My view:
Iron man: Pro Registration leader
Captain America: Anti-Registration Leader
Now that that's out of the way...
Hulk: Iron Man (Whoever has him pretty much wins, unless the other team has hulkbuster... he likely will side with iron man, which means either cap will have to steal hulkbuster, or hulk will be removed in age of ultron, or near the beginning)
Black Widow: Could go either way, likely will go with iron man. (she is more of the, follow my own orders, someone else can control what I do)
Nick Fury: I think he learned his lesson in Cap 2, it's too dangerous to give too much power to one govt or organization. Likely will side with cap, probably will be undercover for most of the time, may not even reveal to the public that he is alive still.
Thor: Iron Man, he needs the earth protected without him having to be there. The freedom of superheroes who live on earth is not of his concern, the safety of earth overall is. Him and iron man are the most powerful (after hulk of course) which means Cap and his team will have to go undercover to not be defeated easily. (My theory is that thor will be trapped without power in the vibranium cave/mine when trying to stop ultron from getting it vibranium. He would be disabled and would not come into play until after civil war has broken out. POSSIBLY: Cap will go to the mine to find thor, thor will not be able to use his own hammer, cap will wield it for him. When thor gets back he learns of the war and joins stark, but wont have any powers other than being an asgardian. (which means he lives long, and has some regeneration powers) OR Iron man will find thor when trying to get vibranium for his own upgrade, he will take him away along with some vibranium, cap will go there to try to stop iron man from taking vibranium, may or may not stop him. For sure iron man will leave, and cap will see the hammer left behind, and he knows or thinks he can lift it, takes it and leaves.
Hawkeye: He will likely be in the movie as one of the scenes is at his farm er whatever... my guess is he will go with romanov, which means stark all the way.
Falcon: In the comics he switches sides at one point, but in the movie he will be with cap at least at the end, and most of the movie.
Winter Soldier: Will probably be an important focus, his turning fully good and working with the other avengers needs to either happen in age of ultron, or civil war. If in civil war he will definitely side with the captain... he has had the experience of a government entity controlling him and he doesn't like it. Why would he give up freedom now that he finally has it? Besides... he's Steves best friend, of course he'll stick by Roger's side! (His role will also be important if say... capt america 4 will end up not having steve rogers in it... for whatever reason... not implying any bad outcome of the war or anything... just sayin'...)
Colson: If he's in it, he will be with Cap.
Ant-Man: If he isn't in it then that means his movie was a failure... which CAN'T happen.

Assuming he will be in the film, he knows how evil mankind can be, but also knows how government doesn't always know who the real bad guys are... he could easily go either way. (From my little knowledge)
Daredevil: Because of his series being a tv show, he may not actually be in the war. If he is, he will probably go with the cap, because he is kind of an undercover type of guy. He doesn't really follow the law even when it's been made, why would he start following a restricting law that hasn't been made yet? (Again, I have a very limited knowledge on him)
Vision: If the story goes he is Jarvis in robotic form, he probably will side with stark. But if he becomes his own entity, not just a hero to be shown whenever stark is, (kinda like how falcon came with the cap but is his own hero) he fought in a world war for the freedom of people in the U.S., he likley will disagree with stark, as the butler disagrees with him often, even though he usually follows his orders... that is, if my theories are correct, and Jarvis AI is human Jarvis in computer form, and Vision is Jarvis AI in Robot form (Along with the soul gem which gives him morals, and other spiritual human components)...
Spider Man: Will likley be between the fight, more specifically siding with different sides at different times. Maybe wont be in Civil War at all, as the actor may or may have not been chosen yet and they likely have already done some filming by now. If he is in it he may be a key character, showing the struggle of a balance between freedom and government. He will probably look up to both characters, and both will tr to talk him into joining their side. Remember, he will only be a highschooler. It may depend on the actor, as actors sometimes shape the character they play.
Final Lineup (Others included):
Pro:
Iron Man
Vision (If he is controlled by Stark or sticks with him all the time)
Iron Patriot/War Machine
Black Widow
Thor (Absent Partially, may not have powers until late into the war)
Hawkeye
Hulk (Absent)
Scarlet Witch (Saw the mess of ultron in a very bad way, I don't know too much about her.)
Quicksilver (Same as above, except he might not be alive for Civil War if he dies in AoU)
Anti:
Captain America
Winter Soldier
Falcon
Agent Colson
Nick Fury
Vision (If he has the soul of (human) Jarvis)
Daredevil (Really don't know that much about him)
Ant-Man (Same)
Neutral:
Black Panther
Spiderman (Switches sides, or is neutral)
Take all of what I said with a HUGE grain of salt. (Or would it be tiny...)
As stated some of the characters I only know the basic backstory of, and never read their comics.