Answer: Nearly any shade tree will have a relatively large and aggressive root system by virtue of the fact that it needs lots of moisture and nutrients to maintain itself. It will also shade out many plants -- including possibly lawn -- below it. The root systems of trees typically spread about one and a half to twice their branch spread, just to give you an idea of the scale.
In terms of very aggressive trees, willows and silver maples (Acer platanoides) are probably among the worst offenders. The Acer rubrum Autumn Blaze is probably average. Keep in mind however that it does reach approximately fifty feet tall and wide, so it is rather large in time.
I would suggest that you consult with your county extension and/or professionally trained nursery personnel to select a tree that is well suited to the specific site you have in mind -- in terms of size, growth rate, and actual growing conditions such as soil type, moisture availability, and so on as well as resistance to any locally prevalent pests and/or diseases.
Research their suggestions and then select one that matches your personal taste. Good luck with your tree!
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