We don't think your son is being picky. We wish more people would think through all they want from a tree before choosing! Even if it's not possible to have it all, finding the right tree is a lot more likely when you work from lists like these.
To get one thing out of the way right off, for front- and back yard tree and ALL trees: Tree roots do not surface. They grow where there is loose soil, and over time the permanent roots increase in diameter. If the roots can grow only in the top two inches of soil because the ground is terribly compacted, they grow there. Once a root achieves a size greater than two inches in diameter, it becomes apparent by breaking the surface -- but it has not changed depth.
Given loose soil, some tree species' roots tend to descend to greater depth before growing out level but a "shallow rooted" species' roots still drop down to 8 or 9 inches if the soil allows. "Deep rooted" species may go down only a few inches further.
So avoiding the roots-on-the-surface effect is not a function of tree type but of planting technique and continuing soil care. At planting time, loosen the soil to a depth of 18" all around the outer edge of the planted root package so roots can grow out at all levels. Make this loose ring at least as wide as the tree branches an grow in a year (6-12" for a slow-growing species, 12-18" for fast). Then, keep loosening in a larger circle every year -- tree care companies and DIY gardeners can do this by drilling holes 12-1" deep and then inserting an air compressor hose to "Blow up" the soil. You can see the surface bulge a bit as the air forces the soil to fracture. Everything in the area benefits, by the way -- trees, gardens, lawns.
For the front yard, consider:
Hedge maple, Acer campestre. a small maple, 30' tall and wide. Grows 8-12" per year. Like all the trees listed here, has a good form even when lower branches are removed, a process that should begin when the tree is young and low limbs are small, and continue until the lowest limb begins at 10-20' above ground. Gold to apricot fall color. Does have maple seeds.
Threeflower maple (Acer triflorum). Another small maple, about 30' tall and wide, but slower than hedge maple. Lovely red-orange in fall, a bit later than other maples but not xo late as the callery pears including Bradford. Incredibly pretty peeling, shiny cinnamon color bark. We keep one elevated (lower limbs removed) for one client but never throw away the branches as there is always someone who wants to use them in an arrangement. Does have maple seeds.
Since so many small trees have fruits that disqualify them from the list (Crabapples make excellent small shade trees but they fruit; redbuds have copious amounts of flat pea-pod-like seeds some years, etc.) we'd plant a large shrub that can be pruned to grow as a tree. First to mind is
seven son shrub, Heptacodium miconioides. No fall color to speak of but the September white fragrant flowers become tiny but visually mighty pink October seeds and the bark is white and exfoliating -- nice to look at in winter. The plant tends to be an ugly duckling as a youngster because of its gawky branching, but sorts itself out into a nice, high-branched 15-20' tree if pruned as it grows. As we look for photos to post on our Forum with these notes we'll look for B.G.'s tree, which was only 4' when planted but shades a patio just 6 years later. One drawback: Wood is not so strong as maple wood. We’ve seen some ice storm breakage.
For the back yard we'd look at:
A male ginkgo (Ginkgo biloba). Ginkgos grow quickly, up to 18" a year while they are young. (Claims that they are slow growing come from outer space; the growth slows once they mature and spend energy on flower and fruit*, but even then they grow moderately, not slowly.) They have a great spread and can be pruned as they grow to remove lower branches. The fall color is a very clear yellow but it's quick, even a lawn-raker's dream since all the leaves turn during one brief period, and fall quickly. (One year, we saw ginkgos turn gold one day and go completely bare the next. No lie.)
Given loose soil, the ginkgo's roots prefer to grow at an angle down until they reach 12-18" deep, then they grow level. So they are very garden-friendly. Ultimate size may top 70' but when we plant one we think in terms of the planting gardener's tenure and expect the tree to be 20' tall and 30'+ wide in 15-20 years. Very strong wood.
*Ginkgos don't fruit until 20+ years old and then only the females bear the apricot-sized yellow fruit. The males contribute wind-borne pollen; females in the vicinity of a male have fruit but no pollen a fact of importance to people with pollen allergies. To be sure you plant a male, fruitless variety read the label or catalog where males are identified by description and variety name 'Autumn Gold', 'Lakeview' etc.
A lacebark elm (Ulmus parvifolia), which grows quickly, has a graceful wide spread, is easily limbed up for clearance, and drops only papery small seeds in spring and small leaves in fall. The bark is very pretty, especially in winter. Fall color is not one of its attributes. Strong wood, very resilient under the weight of snow and ice.
One of the hybrid red-silver maples, perhaps a male (seedless) variety such as 'Autumn Blaze.' Has the red fall color an relatively strong wood of the red maple but has a faster growth rate thanks to its silver maple genes.
Katsura (Cercidiphyllum japonicum) Fast growing, nice gold in fall accompanied by a smell of cinnamon/cloves from the leaves as they change. Would be branched to the ground if allowed so remove lower branches. Do not buy a multi-stemmed specimen as single stem trees grow more quickly up and do not later have trouble with competition between its own trunks.