The OP is not suggesting changing the appearance of the house.....only modernizing the landscape. Two very different goals :-) And the second not at all inappropriate to the style of the house. ellirih, since you have identified types of contemporary landscaping you admire, find a local designer you can work with and show them your inspiration photos. Other than providing you with more illustrations (not really any sort of real design plan specific to your property) there is not much more you can achieve here. Personally, I would be inclined to remove the current vegetation and start over :-) Neither is it very modern in character nor in particularly good condition.

I tried growing Rangoon creeper in a stock tank in full sun. Even with that large of a container it wilted every day. So if you don't mind watering it often it will do fine. My original plant is still growing in a slightly raised bed with a five foot lattice to lean on. It's kind of like THIS except it is not in full sun which would be the ideal. Mine may get three or four hours of sun, filtered sun at that, and may get watered once every 7 to 10 days. It rarely wilts between times. It's amazingly drought tolerated for such a lush tropical vine. Nothing to be scared of with Rangoon creepers. In my experience it doesn't spread from the roots. The clump will just get larger, and will grow tall if it has something to lean on like a fence, an arch, or up into trees. It doesn't twine, but the long branches will need to lean on something. I've seen photos of it tied to a single post where it will then arch over itself. Very pretty. You can cut off any stems going off in the wrong direction with no damage to the plant.

Whatever colors you choose, get a sample pot and paint a large piece of board or cardboard in that color. Look at it at different times of day since the light changes. We see too many sad posts on Houzz where people have been disappointed in the way a color looks over larger areas, and in outdoor light. When you do your plants, make your beds at least 6 feet deep. That may seem huge, but you need to have the first foot along your house bare, so you can access it for maintenance. Then, any decent size shrubs will probably be about 4 feet wide at maturity. (Check your tag on online where you'll see this information. ) That leaves you a foot in front of the shrubs if you want to plant any annuals. When you plant a shrub that's 4 feet wide at maturity, the center of the planting hole should be 3 feet from your house (2 feet from the center to the edge of the mature shrub, plus one foot space to house.) Before your shrubs are mature it may look a bit bare. Just plant self-seeding annuals in between and you'll plant fewer every year as the shrubs grow. I like annual white sweet alyssum which doesn't have deep roots and won't interfere with the shrubs' growth. Or use native plants that behave the same way. (We don't know where you live.) It's less expensive and more beautiful than mulching a large area with bark chips, and it will come back from seed next year. Google "green mulch" and you'll see what other have to say about this idea. If there is someone in your neighborhood whose front garden you admire, stop by when they are outside and ask about it. I have given so many cuttings and divisions of my garden plants to people. https://www.houzz.com/magazine/new-ways-to-think-about-all-that-mulch-in-the-garden-stsetivw-vs~25100660

Thanks for the replies! I've updated the floor plan in the original post to have the windows. Here's a link to a video walkthrough of it in its current state. https://photos.app.goo.gl/hf2117gjeGXEs42Y6 The building was built in 1986, so building code was much less stringent then. On the kitchen side there is roughly 30" between the two properties, but there is an overhang on the upstairs unit that covers the area where the windows on that wall are, so very little light gets in. There may be more than 1' on the other side, but it's so close that minimal light gets in as the other property is also two stories high. Skylights won't work as this is the lower unit with an identical layout above.