Kentucky coffee trees (Gymnocladus dioicus) are a good choice. They are not surface rooting that makes it so difficult to plant and maintain under. And because their leaves emerge very late in spring, woodland wildflowers and other spring blooming perennials are at their best. Growth medium, about 1-2ft a year.

I second Kentucky coffee tree. After taking a few years to settle in my tree has grown about three feet per year for the last couple years in a decidedly less then ideal spot. They are awkward as youngsters but great later on.

Similar, but with a finer texture is honeylocust. They are more widely availble, almost on the verge of overplanting.

Oaks are good to plant under but resent alot of disturbance of their roots.

Birches have the advantage of growing quickly and creating a fairly light shade but do compete somewhat with perennials for water and nutrients.

In my experience elms and maples are the greediest and hardest to work under.

Ted