I've got an elm and a pin oak in my back yard. The elm drops the little helicopter things, but not much in the way of causing allergies. The pin oak drops leaves, and not much else. So many squirrels and chipmunks in the area, the acorns never get big enough to fall off.

Both are great shade trees. Dunno how fast they grow, as both are over 20 years old, and if they've gotten bigger since I moved in 7 years gone, I haven't paid enough attention to notice.