1. It's evidence - the tapes of Costello's conversations, Costigan's identity, whatever else would reveal the set-up should he not be alive in two weeks. Maybe Madolyn passed this on to Dignum, although she also has knowledge that Sullivan is the snitch after hearing the recording. 2. It's something precious to Costigan he wants to be kept safe - for instance, the family photos he had displayed on the coffee table of his mother. (In contrast to Sullivan, he noticed and liked the photo of Madolyn as a kid on her bike, so it's something he connects to.) 3. It's something for Madolyn - maybe a letter where he finally opens up emotionally, or reveals his identity. 4. Last will and testament - because he knew he wasn't coming back. 5. Whatever's in that briefcase in Pulp Fiction. As to the baby...again, no definitive answers. Madolyn might not know. She clearly isn't interested in having Sullivan be part of it after she finds out who he is (she ignores his question "What about the baby?" after Costigan's funeral) so it seems unlikely she would have forced him to raise another man's child in happier circumstances. But my feeling is that we're meant to think it's Costigan's because we only see a sex scene between the two of them. She and Sullivan go on a date, move in together, share a bed, and argue - but are never seen having sex.

It was a very nice film :)