Just a couple of general comments. You don't give us your zone or your general geographic location, both of which we need. And we don't know anything about the orientation of your home. But here are some general thoughts about locating trees.

You'll want to be able to actually use decks/patios and you might want shade on your house too, so for shade from the hottest sun of the day, site trees to the W/SW. For morning shade, site them to the E/SE. Site large trees at appropriate distance from house and place smaller trees alone or in groupings between large tree and house. Smaller trees will also offer some shade on patios/decks when properly sited. (Of course people use shade cloth, but nothing provides cooling like layers of leafy shade.)

If environmental concerns are important to you, the most important tree you can plant is an oak since, as Doug Tallamy explains it's a keystone species. (Link is at Doug Tallamy explains. Don't know why Houzz no long puts links in color)

First off, your grass looks GREAT! ❤️

Secondly, it took me a bit to figure out that this one is your yard (marked with an X - is that correct?)

Third - we need more geographical help. Does your house face north, south, east, or west?

Fourth - are you planning areas for specific purposes like kids play, dog containment, hot tub, etc.

Fifth - the blue circled area around those utility pipes looks like a prime spot for a flower/shrub/ornamental grass bed so you don’t have to mow there.

An Autumn Blaze Maple as it matures (40-50’ tall, 30-40’ wide) may dwarf your house and front yard and its root system make it impossible to maintain a green lush lawn beneath it. There are other trees with foliage color to consider instead.

Your backyard would look great with some smaller trees at the perimeter to screen the neighboring houses.

Before you plant, are there any hardscape, irrigation, etc. to be installed to take into consideration?

Thanks so much, everyone, this has been really helpful! I'll try and answer everyone's questions here in one go.

I'm in Johnson County, Kansas zone 6a, and the house faces south, so the front yard gets strong sun most of the day. And to clear up the photo confusion, the yard marked with the X in littlebug's comment is my backyard.

What I'm going for is a yard that looks striking, especially with color across the seasons. The big thing I'm still torn on, and would love thoughts on, is whether to plant one large tree or a grouping of several smaller trees in the backyard. The idea of a large tree with smaller trees between it and the house stuck with me, and I'm leaning toward some version of that: a larger anchor tree paired with a couple of smaller flowering trees to stretch color across spring and fall. The exact species is still something my wife and I are finalizing, so all suggestions are options I'm weighing.

On placement, thanks for the logic on siting for shade. My west neighbor has a large tree that already shades my afternoons, so I plan to nudge whatever I plant toward the southeast so it still gets good light instead of sitting in that tree's shadow.

On the lawn, I know I won't keep lush grass directly under a big shade tree, so the plan is a mulch ring under the canopy from the start and turning that footprint into a bed rather than turf that I'm fighting to keep.

To whoever asked about hardscape and irrigation, great question. Nothing new is in yet, but if I add a sprinkler system, walkway, or edging, I'll do it before or with the planting so I'm not digging through an established root zone later.

The corner of my backyard, circled in blue in littlebug's comment, has 3 spots for electrical utilities and cable network access. I love the idea of turning it into a bed to stop hand trimming around them.

On privacy, honestly not a big driver for me. Color and overall look matter more to me than screening, but having some bit of privacy with some larger trees would be nice. I'm not particularly after lining my fence line with tall, full trees to entirely block out my neighbors.

Some smaller trees you might like - Kousa dogwood or serviceberry. Kousa dogwood can get pretty big, so best used in a corner, and out from the fence. I l

Sorry, this app no longer lets me see the text as it wraps! (And apparently I’m not the only one with that issue!). I like the serviceberry trees because they don’t get too large and have multiple stems that give lower branching. They have white flowers in May (don’t last long, though), followed by nice green foliage all summer and turn a burnt orange in the fall.
They do produce berries, but the birds seem to do the cleanup.