some ideas:

Ok here is a photo... I hope

We also need to know your geographic location before we can make meaningful suggestions :-)

btw, the suggestion to use Houttunyia cordata is a very ill-advised one. It is an extremely aggressive spreader, will not stay confined to the area and is virtually impossible to be rid of once it is firmly established. There have been countless threads on these forums from homeowners doing battle with this thug!!

Also, hypericum needs full sun and is prone to a very disfiguring rust issue. Also extremely aggressive.

That slope doesn't look steep or large enough to be an erosion issue. I would think that any low growing (and preferably evergreen) but well-behaved groundcover could work very well. But again, we do need to know where you are to make informed suggestions.

Houttunyia is something one plants only if they have no interest in planting ANYTHING else. Ever! I tried that cute little thing many years ago and what I saw it do in a very short time scared me enough to get rid of it ASAP. It might be fine in a wild, no care place.

Doug can justify his suggestion all he wants but the issue remains the same.......anyone who has intentionally or inadvertently planted this pest has lived to regret it. Many consider it the worst plant on the planet, even over and above kudzu!! Houttunyia cordata problems.

This is in Virginia, and that slope is steep. You are practically on your hands and knees going up to the top. Ideally I would like something that requires very little care--no pruning, deadheading, etc.

I'd suggest Pachysandra terminalis for the shady areas and Cotoneaster dammeri for the sunnier location. Both are evergreen, rapid but not aggressive spreaders, require minimal maintenance and are recommended by the Virgina Tech extension service.

Good suggestions all! Is the Cotoneaster dammeri deer-proof?

It is in my neck of the woods!! (I should edit that to say deer resistant.....nothing is truly deer proof!!)

Rarely is it touched by deer, but is a notorious leaf catcher. However, it will contain erosion.

but is a notorious leaf catcher--OK, how will it do if we have a leaf blower/sucker? Honestly, I love the Cotoneaster d. but that could be a dealbreaker.

If you don't want the cotoneaster, then use pachysandra in the shady part and Geranium macrorrhizum in the sunny.

I know nothing about deer resistance, but in addition to the pachysandra and perennial Geranium suggested, look at Geranium Biokovo, old fashioned daylilies (which will need removal of old flower stems once annually) and Centaurea dealbata.

Use a highly texture mulch such as arborist’s chipped trimmings or gorilla hair or shredded bark mulch to help reduce weeds, hold moisture, and reduce possible erosion while plants fill in.

Cotoneaster is used extensively as a GC in my area and I have never seen it be an issue with leaf collection any more than any other evergreen GC!! A leaf blower once or twice a season may be helpful but unless the area receives piles of fallen leaves, they generally just breakdown and decompose over winter and vanish by spring.