We need to know where you are located - plants suitable for Georgia or Oregon may not work well in Michigan or New York.

For the most part, grasses want full sun. There are some species that are more shade tolerant but they tend to be rather low growing and lack much screening ability.

Woodland or part shade shrubs are your best bet. I would look at a mix of both evergreen and deciduous.

I can't give you specific recommendations on plants, but I will say that to get an attractive border you need to have different levels of plantings - at least three. Since it's expensive to buy plants to fill in as large an area as you have, develop a long-term plan and then take a couple years to fill it in. These type of borders will add to the value of your home and reduce the area needing to be mowed. Your other option of course is to put in a wood fence. They can be more attractive than the plain slat fence which is visible in one of your pictures (might be your neighbor's). If you do that, be sure you know exactly where the lot line is. We found out right when we were selling our last house that our fence meandered around the lot line (the previous owners had installed it) and it caused a bit of a kerfuffle before closing.

Arrowwood viburnum and Bayberry should be deer resistant and be okay with shade. Of course, it depends on how much. That said, hungry deer will eat anything.

Central New York State is my location! Thank you for the ideas. Partial shade shrubs sound good and I like the idea of combining deciduous and evergreen. I am avoiding a fence, as the deer wander through the borders of our backyards and I kind of like them having access to that path. Even so, I wonder if I put up a few grids between the trees if ivy might grow. I looked up your suggestions. Japanese Laurel, yes! Arrowwood viburnum & Bayberry, sweet! Tiny Tower Arborvitae is not an option, unfortunately, as there are power lines running through and the electric company will chop off tops of trees within leaning distance. ...am a bit limited there. Yes! Thanks for your reminder to layer!

How about some cornus kousa? They can grow as understory.

Please please don’t plant ivy. If you could see how many hundreds of trees it has ruined here in our current town of Lexington VA and in previous town Opelika /Auburn AL and I am sure many many other places. it is a scourge and impossible to control or kill.

Ivy! My oh my, how could I even consider ivy! I purchased my home 12 years ago, originally Engulfed in English ivy. Thank you for the reminder Not to get mixed up with it again. :)

Before (When I removed all the ivy, the entire structure was dingy-gray and infested with critters. You bet ivy ruins everything to which it can cling!) I must say, I am quite proud of my hard work below. :)

After! (I hand-stained each and every stone, then used gloss sealer!)

I second dogwoods and layering with other understory shrubs and trees and perennials and, if you are OK with big trees, hemlocks.