We have a great fact sheet on deciduous trees for Oklahoma that you can review to see if one stands out to you - Selecting Deciduous Trees for Oklahoma. Something important to consider when choosing a tree is the space and location for the tree. There should be adequate space for the top growth but also root growth. Be aware of the mature size and shape and do not place it too close to any structures.

There are many oaks, many native to Oklahoma. They make great shade trees but remember they also produce acorns. 

For additional assistance you can also reach out the Payne County OSU Extension Center - https://extension.okstate.edu/county/payne/.