Answer: To some extent the selection will vary depending on the kind of tree you are planting beneath and how large an area you need to cover, how shady/sunny it is, whether or not you want an evergreen. Most trees object to having the soil around and over their roots disturbed, oaks and dogwoods for example are very sensitive to this. A few trees such as maples tend to have very aggressive roots that will starve your plants of water and nutrients. In any case you must not heap soil or mulch up against the bark of the tree as this will casue the bark to rot and damage the tree.
A few groundcovers to consider might include ajuga and English ivy (both available in colorful variegated cultivars) along with containers of colorful flowering annuals such as caladium or impatiens for added color in summer. Periwinkle or Vinca minor is a glossy evergreen with blue blooms in the spring, Liriope is a grassy textured groundcover that might work for you. There are many different plants you could use.
Your local professional nursery staff may have other suggestions based on a more detailed understanding of the planting conditions and your design goals. Good luck with your project!
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