I just thought about 3 pretty interresting ideas for beginning the Campaing.

1. If you start as a Crusader an Inquisitor calls for backup to purge a world (or whatever) and your fleet answers. During the Mission you support said Inquisitor and as a reward he asks you to follow him.

2. If you start as an Assassin your Job is to eliminate a target which is currently observed by the Inquisition. After finishing the Job you get cought by the Inquisitor in charge of the observation and interrogated. He gives you the chance to support him to secure the sector to pay your debt...or get executed as a traitor. 

3. If you start as a Psyker you are currently on one of the Black Ships heading to Terra. During the Warp transition Demons attack the ship and corrupt most of the other Psykers. However you are strong enough to defend yourself against the Demons and fight a way through the ship to support the troops on board. After the Demons have been defeated everyone on  board will be interrogated by the Inquisition and you are asked if you (as a A+ Psyker) want to join the Inquisition and help to secure the new sector.

I'm sorry if my English is a bit strange, but it isn't my mother language.