I'm also just getting into Marvel canon, so I had to sort of make a list of what was what. In a lot of cases, just be aware that you'll be reading something, and then in the next tie-in the events of the last haven't happened yet, etc. It can get a bit confusing, but as long as you know the general time-line, you should be OK.

Also, what I found frustrating about CW was that the culminating event, Steven's death, wasn't in any of the stuff labeled Civil War, so the main book ends, then you cut to, say, Tony's Civil War tie-in and at the end Steve is already dead.

So my advice, based on what I read, would basically be:

Civil War
Captain America #25 (if you're just looking for the event itself)
Civil War: Captain America
Civil War: Iron Man
Anything other CW tie-in you're interested in. (I liked the New Avengers stuff.)
Fallen Son


If you're interested in Iron Man stuff, I made a list for myself to figure out what goes where of recent canon, most of which ties in with Civil War:

Extremis (issue #1-6)
Execute Program (7-12)
CIVIL WAR HAPPENS HERE
Civil War: Iron Man (13-14, Casualties of War, The Confession)
Director of SHIELD (15-18)
World War Hulk (19-20)
Haunted (21-28)
With Iron Hands (29-32)

ALL THE SKRULL STUFF (which I've yet to figure out the right reading order for)

Invincible Iron Man (Issue #1-19)
Invincible Iron Man: Stark Disassembled (#20-24)
Invincible Iron Man: Stark Resilient (#25-28)
ETC