Answer: Generally speaking, you would have layers of plantings such as those you described, done in a way to mimic how nature places plants. Tall trees with understory trees toward the lawn side where the light is naturally a bit brighter, beneath and to the front of the trees a layer of shrubs and then finally lower growing plants. Sometimes the lower growing plants can be flowering perennials, or you could use a more traditional groundcover such as Vinca minor.
The ground cover can extend back in under the mature trees, or can be mingled with shade loving perennials there. You might use a mulch of leaves and bark there as well, with perhaps a pathway and a bench to create a pleasant scene. The mass planting layer can be done in all one plant or in drifts of plants and can extend as far as desired out into the lawn area or even replace the lawn. As it becomes sunnier, you will need to shift your plants from shade lovers to sun lovers. You might use a water permeable paving area to provide for outdoor sitting, dining or entertaining space to serve as a bridge between the lawn and the woodsy area.
I hope in clearing the brush you did not inadvertently remove desirable plants that were well adapted to living there. You may also discover that some natives naturally re-appear in the opened areas. Some plants will grow well in deep shade while others prefer dappled light or morning sun. Direct afternoon sun is stronger and hotter than morning sun, so a different selection of plants would be required in that exposure.
The plants you use will depend on not only your design goals but also on the growing conditions in that area of your yard. You may find it difficult to plant beneath mature trees if they are surface rooted trees, or you may find that due to the trees the soil there is very dry. Or, you may find that the drainage pattern of your yard directs runoff to that area so it tends to stay moist. You will need to find out what kind of soil is there, as well as how shady it really is in the summer time growing season. You will also need to decide on how much effort you are willing to put into establishing and maintaining the planting.
I would suggest you work with your local county extension and/or professionally trained nursery staff to develop a plan for that area of your yard. They should be able to help you analyze the growing conditions (including running soil tests) and identify plants that would grow well there, then you would select the ones you like best from among those. If you are planning an extensive project you might wish to hire a consultant or designer who can assist you in more detail. Best of luck with your project!
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