Hmmm, I wish I still had the songlist I used for a similar sort of thing. I am a huge fan of Bob Dylan (two more days until I see him live), as some people might have noticed. Songs like Just like a woman (listening to it now), Don't think twice, Lay lady lay, the songs of his that don't have the all too familiar 1, 4, 5, that make many of his songs sound the same if you don't have a lead guitarist playing any unique lines. Autumn Leaves, Gee Baby aint I good to you, jazz standards like that are good if you are into that kind of thing.
Ummm, looking through some of my stuff....
The Boxer is a great song, specially to get people singing along, heaps of people know it. Also, Neil Young songs, like Old Man, and The Needle and the Damage done.
Can't think of many more at the moment that work for solo and voice, but I hope this helps.