There are plants for every type of garden be it blazing sun, dark shade or damp to wet, what you may need to do is prepare the soil before you plant as wet / shaded soil can become very smelly, when I had an area like that years ago my Dad made me add loads of charcoal to the soil as he said it would help to keep it sweet, I think that was a polite way of saying it will NOT pong now LOL.
Look in the garden centre for the plants you want, take them off the shelf and sit them together in groups to give you an idea of the different textures, different shades of green and ofcource the different leaf shapes and flowers. it will help you know what you like and dont like before you spend money on plants that are not exactly cheep when you need several, I like to plant each type of the same plants in groups of 3-5-7 as this gives a better spread instead on one of each type that can become lost in among thicker plants or taller plants once the begin to mature.
Look on the label to find out the planting distance required between each plant, how tall and write labels when you start to plant, you can lay the purchased plants out again in your garden so you know they look right together, move if required and make sure you stand back as you go so your happy with the way they are looking in situ.
My list would have to be:
Hazel, / Cornus, the type with the coloured stems, cut back each spring and new colours regrow. Red, Yellow, Black and green.
Astible, fluffy flowers in Pink, red, Cream, nice foliage too.
Hosta's (some that require wet rather than damp) all sizes, leaf colours and love the flowers of lilac / pink. SLUGS / SNAILS love them so protect them.
Iris, (some) some are for damp / wet areas where as some wont be able to cope in wet.
Polyygonatum, (some) for damp / wet soil.
Mahonia, Leaf like Holly and lovely bright Yellow flowers in laTE SUMMER.
VIOLA, (some) AGAIN THERE ARE SOME SUITED TO DAMP SOIL.
Some of the plants may have to be set in soil where there is NOT too much wet at their feet but you can adjust the soil by adding small grit to help drainage in areas where toy need drier conditions.
Give some root cover with leaf mould in winter IF you get ground freezes.
The other option is to find a way to drain the water, or make the area higher, build up the soil into a mound so that it is not so wet all the times.
This can be pretty easy if the area is pretty much wide open, just add a blend of soil and compost until the water runs off somewhere more appropriate.
This can be next to impossible if there are already established trees and shrubs nearby. These plants will not want additional soil added around their trunks. So adding soil to the wet area would make these plants the low place, and they would not like that!
Install drainage, including a sump pump, if needed, to remove the water.
Do you know the source of the water? Is there an underground spring or a broken pipe? Is it a low area that floods when it rains? If there is some way to divert the water before it starts making the area so wet, that would help.
Here are some odd answers to the source of water question that I have seen over the years:
There was no problem when the house was built, several dry years, too, but earthquakes opened some passages underground, on the hill above the house. Result: The sunken fireplace was 6" deep in water. Solution: French drain 2' deep all around the house. Went back a few years later and the drain runs even in the hottest, driest summers. But the sunken fireplace is dry!
Actual artesian spring on the property. A path north along the fence then east was so soggy wet and water running all the time that we had to build mounds and plant the more water tolerant plants in that path. We also included an extensive drain system. But we made use of the water, too. We installed a very large subterranean tank and use it to irrigate the dry parts of the property. The kicker: The system ran dry! We had to cross over to municipal water for the irrigation.
Wet area in the yard, near the bottom of a retaining wall-fence combo that separates the property. Answer: uphill neighbor's spa was leaking.
Anyway, back to your question:
If you go to the local nurseries and see all sorts of plants for shade, ask which require the most water, or which are better for dry areas. Then get one each of perhaps a dozen plants that are OK in the wet spots, and try them.
Prepare the soil with lots of compost (unless your soil is already high in organic matter) and make some mounds for each individual plant.
If it is a pond plant or a marginal (a plant that lives on the margins or edges of ponds) they you probably do not have to worry about a mound.
I think deep shade is going to be hardest to solve. Is it trees? Can they be thinned out?
Lobelia 'Cardinalis' (Cardinal Flower) bright Red mid-to-late Summer blooms
Hosta (comes in about a zillion varieties)
Astilbe (many varieties)
All can go from full sun to full shade. All three lived under about 3" of water for about two weeks early this spring after extremely heavy rains flooded the back portion of my back yard. As soon as it warmed up a bit, they grew and thrived.
Hummingbirds like the blooms of all of these and absolutely adore Cardinal Flower.
The following link is from PlantFiles for Cardinal Flower. There are quite a few pics and comments you might enjoy. A quick glance at how many members "have or want this plant for trade" should give you an idea how popular it is.