Answer: I think Vinca minor or periwinkle would be your best bet for shade, it is a traditional groundcover with evergreen leaves and blue blooms in the spring. It grows relatively quickly but will still need a few years to fill in completely. It should be widely available as inexpensive small plants for just this purpose in the spring. Plant them about a foot apart and mulch in-between them, plan on watering them the first year until they become established.
In my experience those little plugs would be too small for a fall planting this late in the season because they would frost heave when you have the freeze/thaw days in late fall and early spring. You could probably still plant larger ones though, if you can find them for sale at this late season.
In the meantime you might want to try to plant some fast growing annual rye grass to hold the soil (this will freeze to death in winter and add organic matter to the soil so it is beneficial in two ways) or possibly mulch the area to try to prevent erosion this winter. Larger particles will stay in place better on a slope. You might also try terracing it a bit with boards for example to slow the runoff. If the hill is steep you may also want to check with a landscape architect or engineer or other trained professional with experience in drainage to make sure it will stay stable this winter and during the snow melt/spring rains.
Good luck with your project!
Q&A Library Searching Tips