A mix of groundcovers would be a good choice since the use of multiple species would help to make the planting more resilient long-term, such as if facing a pest or disease outbreak or unusual weather which causes plant stress or damage. Using predominantly native species would be ideal, but anything non-invasive that suits the site conditions can work. Conditions to consider when selecting candidates include how much summer sun the area receives (you  mention shade, and if it gets at least a little direct light during the day, that helps to keep your options more diverse), soil moisture levels (sounds like it can get a deluge, but might not stay wet for too long), and if deer will browse the area. Below are some starter ideas, but it's far from an exhaustive list.

Until you can plant, or plant in stages (especially if you eventually want to terrace it), a good erosion-alleviating cover would be arborist wood chips as a mulch. This tends to be better for the soil when needed in thicker layers than bark mulch, and is sometimes much cheaper to come by in bulk as well. (That said, full deliveries can be large and more than you need, so perhaps there are other gardeners you can share it with, or use it to mulch other parts of the garden.) Otherwise, using a permeable, organic (biodegradable) mulch "blanket" by means of a woven or spun material might be useful to also help prevent against rapid erosion. (Like the mats used to cover grass seed; they might be made of wood excelsior, coconut fibers, untreated burlap, or other natural materials.) Pinning this cover down might help to hold the base layer of a wood chip mulch in place, or at least lessen erosion when used by itself, and should be able to be planted-through as-is without having to remove it, as one should if using synthetic landscape fabric.

Keep in mind that few or no groundcovers are highly tolerant of regular foot traffic, so include a mulched or stone-paved path (or steps) if you regularly walk through this area. Only turfgrass adapts well to human or pet foot traffic with minimal damage, though it's too shaded there for turfgrasses to grow well, erosion notwithstanding.

A few native plant ideas:

• Golden Ragwort (Packera aurea) - aggressive; evergreen
• ferns like Sensitive Fern (Onoclea sensibilis) and Hayscented Fern (Dennstaedtia punctilobula) - both aggressive, and the former can handle more evenly-damp soils; other ferns should also do well, but may not spread much per plant
• White Wood Aster (Aster divaricatus, also named Eurybia divaricata) - can self-sow into patches
• Blue Wood Aster (Aster cordifolius, also named Symphyotrichum cordifolium)
• Creeping Phlox (Phlox stolonifera) and Wild Blue Phlox (Phlox divericata) - somewhat slow to spread and semi-evergreen; fragrant blooms
• Pussytoes (Antennaria) - best for areas that don't stay too wet
• Wild Ginger (Asarum canadense) - slow spreader
• Sedges (Carex, several species) - some of these grass look-alikes spread faster than others, though usually by seed or runners into a cluster of clumps rather than a solid lawn-like look
• Crested Iris (Iris cristata) - slow to moderate spreader; one of the only irises that handles shade well
• Black Huckleberry (Gaylussacia baccata) - short, slowly-spreading shrubs that look a lot like wild lowbush blueberry
• Leucothoe (Leucothoe axillaris or L. fontanesiana) - evergreen; can sucker a bit to spread, but mainly helps to reduce erosion through arching stems that give it a wide footprint

A few non-native plant ideas:

• Barrenwort (Epimedium) - slow to spread, sometimes evergreen
• Mondo Grass (Ophiopogon) - slow to spread, and available in a dwarf form that stays very short; provides a lawn-like look in dark green year-round, but does not need mowing
• Sweetbox (Sarcococca hookeriana humilis) - slow to spread; evergreen; fragrant blooms in late winter or early spring

Due to their invasive behavior, we recommend you avoid using Japanese Pachysandra (also called Spurge, Pachysandra terminalis), English Ivy (Hedera helix), Periwinkle (Vinca major and Vinca minor), and Bugleweed (Ajuga reptans), even though several garden centers if our region still sell them as groundcovers.

Miri