Answer: It would help to decide at the outset if you want it to be formal or informal and then try to come up with a theme or overall style for the planting, preferably something that also blends well with the rest of your landscaping.
You will need to select shade tolerant plants, and probably limited to those that can tolerate drier conditions since it is under trees and also raised which tends to drain well. Keep in mind too that the soil in the bed will probably settle over time, so you may need to remove hard sides or otherwise change the edging to accommodate that. Annual mulching with organic mulch may help slow the process.
If it is a formal area, you could surround it with a small fence or stone wall and/or low clipped hedge to accentuate the rectangular outline. If it is informal you might soften the edges with trailing plants. Since this is a large space, you could conceivably add a small stone or brick or gravel patio with bench or birdbath or urn to the center as a focal point. At 20 by 15 feet, you could actually put a pergola there and use it as support for Clematis as long as the area receives bright dappled light.
You might use boxwoods or yews at the center of the design, surrounded by shade tolerant perennials such as hosta and/or groundcover such as Vinca minor. Other groundcovers to consider would include liriope and ajuga. Small early season bulbs such as Scilla sibirica or Chionodoxa or Snowdrops could also be planted there. Additonal shrubs to consider might be Euonymus fortunei, Kerria japonica, and Chaenomeles. These last two will not bloom as heavily in shade as they do in sun but they can be very pretty in a woodsy setting and will tolerate drier soil.
If you are able to water the area so the soil stays evenly moist, you could consider using azaleas as well as long as the spot is not windy in winter.
Your local professional nursery staff may have additional suggestions. Enjoy your new planting area!
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