Does your road ever get plowed to clear snow in winter? Ever get salted? If the answer to either question is yes, you don't want shrubs, especially evergreens like boxwood between the road and the fence. Also, how much room is there? I am not entirely sure that there is room for boxwoods in that spot unless you want to learn how to shear them when they start to get larger a few years down the road. Do folks ever park along the road? If yes, how would a passenger get out of the car?

While what you have there may have gotten weedy and out of control, there may be other perennials that will do well there if you plant just a couple of types of hardy, dense-growing perennials such as one of the groundcover perennial geraniums. Regardless of what you have there, it will need something for weed control, but which plants you choose may increase or reduce the amount of weeding. The easiest is grass since all you have to do is mow and weed whack along the fence. Dense growing perennials of just one or two kinds might work. If no snow, some densely growing shrubs might work if well-mulched. Regardless, anything other than grass will need some weeding, at least for a while until it fills in, and even then will need some a few times annually based on my experience.

For your backyard, are you interested in tall deciduous trees or evergreens, or do you want shrubs? Or some tall and some shorter plants? Is it more that you don't want to see all of the neighbors' yard or just all of the fence? Do you want year round coverage or is that not important?

emerald green = smargrad == the usual/common suspect

green giants= green giants ...

no such thing as emerald green giant ...

you do not have room for green giants ... unless you are willing to give up space .. both in height and width ...

if you plant boxwood ... you are signing up for a lifetime of shearing/pruning ... imo ...

ken

Thank you so much for all your comments and input. This is extremely helpful! We'll check out the plant/trees that were mentioned. In the front, I guess we either have to commit to putting the work in to maintain the plants or go with something that may not be our ideal look. (We do get lots of snow, although they don't do a lot of treatment in our street as it is a small roundabout with minimal traffic.)

For the backyard, it sounds like green giants will take up too much space and get too tall. We are not trying to completely block the neighbor's yard (so it doesn't have to be too tall), nor does it have to cover the fence completely. We just wanted something green that would at least create some visual distraction from the bare wooden fence they are planning on putting up. It sounds like maybe a shrub may be better for this purpose.

Green Giant would NOT work in front of the fence. Boxwood might, but I personally dislike boxwood. (A mater of personal taste. Plus it is being plagued by a blight in parts of the country and is an invasive species in parts of the country.)
It's a matter of how high the plows pile snow on it. Something that can be leveled to the ground and grow again, like Diablo Ninebark, might work. Or perhaps creeping juniper?

Didn't even realize you were considering Green Giant for the back fence...you said you didn't want something dense, and arborvitae is as dense as it gets.
Trees might work there. Remember...shrubs often take up way more yard space then large trees, because large trees only take up ground level space as wide as their trunk, and you can walk under the branches. Just no conical trees.

Could you post a picture of the back wooden fence aken from the opposite side of the yard? In the photo you posted is it to the left, right, or behind the photographer? I'm having trouble visualizing what we are looking at.

Buxus invasive?? That's a new one for me and I'd like to see some substantiation of that for confirmation. But I agree that boxwood is not a great choice for that location unless you are very careful in selecting blight resistant varieties....the blight is pretty rampant in that portion of the east coast.