If moisture is getting in it won't make much difference what kinds of plants you have. You need to make repairs to your home before you replant. Also, make sure to look for plants that don't have widespread root systems. They can do a lot of damage and create more problems.

You had moisture problems due to the shade. I can't tell from your photos, but if you've pruned your shade tree and the large bush, you'll get air and light to the rest of the garden. Plan for your garden to fill in as it matures, so don't put anything too close to your foundation.

I think you need to check your gutter situation and prune back or remove that tree next to the walkway before you bother planting anything back there.

First step is address your water issue, I'm assuming this is actually yours and not a rental here. Like others said, lack of sunlight is probably an issue here. If cutting back that (lilac?) tree will give you direct sun there then do it.

Get yourself one of those big pots in a bold color and place in front of your chipped mess there. Plant a nice topiary evergreen thing in it. Mulch the dirt bed.

Plants don't cause water damage.

The problem lies elsewhere. Drainage? Gutters? Downspouts?

Perhaps a concrete apron extending a foot or so from your foundation (and sloping gently away from the house) would help. Or a system of stones overlying a plastic sheet to act as a water barrier. Good luck!

Liriope (also known as lily turf or monkey grass) is a reliable drought hardy shade plant where nothing else grows. Care is super easy, cut it down to the ground in late winter to get rid of the raggedy growth from the previous year before the new growth comes up. The trick is to plant is it really close together so it looks like a sweep of grass rather than the sad plant here, plant there, you often see in commercial properties. It comes in green, white and green varigated one and a creeping one (liriope spicata). Flowers come in purple, white and pink.

rustypatina sounds right on track. here in NYC what is often needed is called "french drain" you excavate down several feet in wide swath out from the building and install gravel so that rain water drains through and below/beyond your foundation.

I agree that we would need to know what the moisture problem was before giving accurate advice.
However, if you want a flower or herb bed instead of a shrub this looks like a good place for a planter box made from an old filing cabinet (described in A.T. article). Do not place it right up against house wall , leave some air space.

If you have moisture damaging your home it is probably the result of improper drainage/grading that is leading to water draining into your home rather than away from it. As a previous commenter mentioned, you may need to hire a contractor to take a look and possibly install a french drain or other mechanism for diverting stormwater. Plants are actually often the solution, not the problem, because they absorb water that runs off from your roof or from a higher grade in your yard and slow down the flow of water during storms. Other stormwater techniques such as rain gardens sited AWAY from your foundation, rain barrels attached to your gutters, etc, can also help.

Before you plant anything, have someone examine and address your moisture problem. Then plant whatever you want there so long as it works for your climate and the amount of sun you get.

If you are having moisture problems have a contractor inspect your foundation before you plant. It wont matter what you pant if there is already damage. I would also ask them for suggestions on drainage. Once you have that done, just plant some annuals that like the shade, like impatiens.(Because it looks like a very shady area in the pic) Their roots don't go down deep enuff to hurt anything. They are generally pretty easy to grow.They are easy to find. They are cheap. They tend not to get alot of pests (aphids, scales fungus ect) like roses. They tend to like any sort of soil. Even soil they are supposed to like. They come in lots of colors. If they do well you can add a trellis and they will climb it. In the fall you cut them back and let them die off. Then you have a perfect spot for Halloween pumpkins. Then it becomes a perfect place for a small christmass light display or something. Then come the spring you just plant again. They dont need to be fertilized regularly either. You can by potting or top soil with time release fertilizer in it, when you plant them and that is about all they will ever need. Depending on how dry it is in the summer where you are at you might not even need to water regularly. I have to water mine about every 3-4days and I live in southern California. Its very dry out here. My mom doesn't bother to water hers at all she lives in Michigan. For her she just lets them grow.

Another vote for "it's not the plants, it's the drainage." (Although WATERING plants might exacerbate bad drainage.)

Fix the drainage and any water damage to the house, then consult with a local nursery about what plants are suitable there. (Advice is free at the nursery -- bring along photos of the spot.) A lot depends on your location, but in my area, since that's a shady area, I'd go with shade plants like ferns, hostas, impatiens, spring bulbs, etc. depending on what you want to achieve.

Dutch Flag iris love damp environments, and will soak up any water that is in the soil. (They are often used for natural pond filtration and bank erosion control.) You'll never have to water it, and it will take care of any excess in the ground. Once it's established, you pretty much ignore it, and the flowers are gorgeous!