Geranium macrorrhizum (Big Root Geranium) should work for the shady area. It would be pretty much evergreen in your area. And it's weed suppressing and deer resistant as well. Morning to midday sun would also be ok for most plants that prefer shade. But if you're talking about a really huge area, I'd be inclined to use at least two different groundcovers. Without a picture and/or rough measurements it's hard to say more.

I've been really happy with Sarcococcas humilus on a site similar to description. A bit slow to spread to total coverage, but a nice low evergreen that has good weed blocking coverage. Another for such a site though not evergreen is Epimedium XFrohenleiten. Lovely dense leaf coverage about 8-10 inch and golden flowers in spring. Seems to like 4-5 hours morning sun but an also stand medium shade all day, and forms a dense root mass that holds back vitrually ever weed around here except garlic grass(Allium Sp,?).