I would start with Dis-Assembled, as where that's where the current Brian Michael Bendis era starts.
Honestly, I'd lead off and go into Civil War off in this order...
Young Avengers: Sidekicks*
Captain America:Winter Soldier 1&2*
New Avengers vol 1: Breakout
New Avengers vol 2: Sentry
Young Avengers: Family Matters*
New Avengers vol 3: Secrets and Lies
House of M
Captain America: Red Menace 1&2*
New Avengers vol 4: The Collective
* Not required but HIGHLY recommended.
**Would you be interested in the myriad tie-ins or just the main story?
There are probably others that other posters might recommend, but this is limited to what I own.
Get back to us once you get this far, and we can go into post CW reading order.