It's a bit difficult to judge with just this one photo of a small space, but based on what you've given for information, I would probably remove all the grass in this area and replace it with shrubs and small trees. Are you wanting privacy on your deck or on the ground level?

Arborvitaes come in a range of mature sizes, but if they are being sold as 6 footers, they will be far too large for that area in just a few years, and then you will need to figure out how to remove them. In 6 years my medium-growing arborvitae selections (Sungold and Techny) have gone from about 3' to 6' and 8', so a full-sized one will grow that much faster. They will get something like 6'-8' wide. So be sure that you get one with a smaller, narrower stature for your small space if you decide to go with arborvitae. They are also loved by deer, so a poor choice if you have deer in the neighborhood since the entire base will be nibbled bare leaving you with twiggy-based lollypop shapes.

Consider some evergreen shrubs (not the trees that a full-sized arborvitae wants to be) such as narrow yews if you don't have deer, or broad-leafed evergreens such as rhododendrons. Or choose vines that will cling to trellises if the privacy is most important in the warmer weather; a couple of Summer Snow clematis would create a nice full screen that will be covered with tiny white flowers for a few weeks, and maintenance involved is just cutting down to 2' or so every winter and removing the trimmings.

We are wanting privacy on the ground level. :) thanks so much for your reply- really helpful info. This afternoon I started to remove the grass.

I love the summer snow idea- I think I'll use them. I don't like arborvitae all that much and have scraped the idea. I think I'm doing with tall grasses now intermixed with some shrubs and flowering perinneals (sage, black eyes Susan, hydragnea bc there is shade in half) I have 3 narrow trellis' I'm placing in the middle.

Do you think I should do the clematis on all three trellis'? Or I was also thinking of an icy. The trellis is to just give privacy in the warm months.

Ivy prefers a solid surface and is a fair amount of work to control in a mixed bed, so I wouldn't use that.

I don't know where you are, but many of the big-leafed hydrangea (Hydrangea macrophylla) are fussy as far as winter or spring freezes killing the flowering buds, and many are short enough to give little if any privacy. If it is bright shade or has some sun, look at panicle hydrangea which will bloom regardless since it sets its flowering buds on the current year's wood. Check out H. paniculata Quickfire (6' in all directions) which will bloom for me here in NH from early July through frost, starting white and then turning pink as the season progresses. If you decide it's too shady for H. paniculata, then be sure you get a reblooming H. macrophylla) that's tall enough to help with the privacy.

You can do 3 smaller clematis on the 3 narrow trellises or maybe 1 Summer Snow (AKA Paul Farges) on your three, if they are spread out a bit with something to link them and a bit of guidance for the clematis to grow sideways, not just up. Summer Snow is quite large - getting to 15'-20', so may be too large since you only want screening for the yard level and don't have a large structure. Look at type 3 (hard prune) clematis since they are easiest to grow, generally speaking, and will be blooming in summer. If there aren't any good nurseries near you with a good selection of type 3 clematis then get some mail-order. Brushwood Nursery is a good source.

You are so helpful- thank you! We are in Chicago.

For immediate results ask the neighbors if you can install screen/slats in the fence. There are many to choose from

http://www.lowes.com/pl/Fence-screens-Fencing-gates-Building-supplies/4294402522