Tree or shrub to plant in moist shaded garden

My backgarden is southfacing and sheltered, but lower than neighbours garden so rather wet at the southern edge. High stonewall to the south, so quite shaded. I’d like to plant a small tree or large bush in the southwest corner, but don’t know what would work with the wet soil and partial shade. Would love something white flowering. “Plantfinder” didn’t find any suggestions. Would a magnolia tree work? Or a big hydrangea bush? Or what else? Would also appreciate help on when to plant and what compost to use around the tree/shrub?