Answer: The east side should be fine for boxwood in terms of sunlight. Boxwoods require a well drained soil, so if it is extra damp or wet there they will not thrive. They also need protection from winter winds. Boxwoods are considered deer resistant.
You will need to use some form of edging no matter what you plant (either a dug edge or a physical barrier), as lawn grasses will encroach beneath the shrubs. Once that happens, you would need to trim the grass and this is a labor intensive chore. Trimming often results in accidental damage to the stems of the shrubs, and if severe enough that type of bark damage can kill the shrubs.
The edging will also help keep the mulch from spilling into the lawn. Whichever shrubs you use, they should be given a year round layer of organic mulch about two to three inches thick. This helps keep down weeds, helps maintain an even soil moisture level, and also helps feed the soil slowly as it breaks down over time.
You would plant the boxwoods (or whatever shrubs you use) far enough out from the house that rain will get past the overhang to water them. Also, you need to be able to get in behind them to do any eventual maintenance on the house.
I would suggest you consult with your local county extension and professionally trained nursery staff to analyze the growing conditions along that side of your house (wind exposure, soil type, and soil moisture, etc.) Based on a more detailed understanding of the planting site and your design goals they should be able to help you select an appropriate shrub. Enjoy your planting!
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