Answer: Based on the description you provided, it sounds like you might want to put an extension on your downspout to direct the water away from the garden area and prevent flooding during rain storms. You could paint the spout to match the exterior of your home to help it recede visually.
In a small area it is usually good to limit your planting to just a few plants such as one type of shrub, one or two perennials, perhaps a groundcover (rather than lawn) and some spring flowering bulbs. Your specific plant choice will depend on whether the spot is sunny or shady (and at what time of day) and the amount of space available for the plants as they grow and mature over time.
In a sunny spot you might grow a low maintenance landscape rose such as KnockOut or Carefree series as the focal point flowering shrub, several boxwoods for background and evergreen effect in the winter, a daylily you especially like, and some daffodils and use ajuga as the groundcover. In a shady spot you might grow a hydrangea, some yews, a selection of hostas, and perhaps underplant that with Vinca minor, an evergreen groundcover. I hope this gives you some ideas.
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