I would maybe start with a wall hanging that is simple for the newbies and those experienced quilters there they could dive into a lap quilt. take a few patterns and let them choose which one they would like to do. this will let them feel in control of their lives. which when they are in homes they may times feel like they no longer have control.
I love the idea of doing a raffle. depending on how often you get there you could do a raffle once a month or every other month when you have a few quilts done. you could let people put their name in a jar for each quilt that they want if their name get picked in one they don't get win any of the others till everyone has won one alteast.