You definitely need to direct the water away from your flower bed first. Go to Home Depot or Lowes and buy an inexpensive flexible extension for the end of your gutter and direct the water out of the bed entirely. If you don't do this, you will most likely have ongoing problems with the soil being too wet at times.
By the time it's warm enough to plant annuals (mid-April/early May), the Hostas will be showing a bit, so you should know where they are located. Definitely ask a local greenhouse/nursery, such as Family Tree, about what plants would work best in dense shade. Their prices are a bit high, but once you know what you are looking for, you can shop around for the best prices. Several other stores, such as Home Depot or Walmart, always carry the standard varieties and have sales running at different times.
Impatiens, Begonias, Coleus (colorful foliage), Caladium (non-flowering but colorful foliage) are all good sturdy annual plants for the shade. They will give you the most color for a longer period of time throughout the summer than perennials.
Again, the nurseries are where you will find the knowledge and expertise you are looking for. Good luck and happy gardening!