I live down in the Midlothian area where the soil is very rocky. I was wondering what the best type of shade trees are available for this type of soil? If someone could help me out I would appreciate it.

Burr oak is the first thing that comes to mind for me. Fast grower, hardy tree, makes for great shade.

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Shepherd of the Trees
It is not our part to master all the tides of the world, but to do what is in us for the succor of those years wherein we are set, uprooting the evil in the fields we know so that those who live after may have clean earth to till.