You're a zone up from me, but you might look at Viburnum prunifolium, Redbud, both natives and spring bloomers and a few of each (don't alternate them), might work. You might also google something like small trees for zone 7 and see what you turn up.

I prefer viburnum rufidulum if you have ample soil moisture vs prunifolium, though both are good choices.
American smoke tree (cotinus obovatus) is a lovely alternative if you have a drier soil.

I'd also suggest (because I'm doing the same ideas up in Springdale as I bought a new house this winter): anerican holly (depending on variety may be eventually huge), chalk maple (small sugar maple native to Oklahoma/Texas/Arkansas), nyssa sylvatica (black tupelo, if not dry)

Think ahead to the eventual mature size of your trees -- I doubt you'd need more than 2 or 3 trees, even if they are "small trees". See those tree crowns in the distance? (Yes, they will get that big.) While planning, think about the direction of the sun and how much shade will be cast by the trees, how much leaf litter will fall, and plan accordingly. The playground equipment won't be there more than a few years -- plan for the future use of the patio.

You can't go wrong, whatever you plant will suit your purposes. plant 4 to 6 trees this year, and then next year, if you have regrets, plant 4 to 6 more!

If the trees are too much bother you can chop them down, or leave it for the next owners to deal with! Really, you will learn by doing, and I think you have the right idea. It will be ten years or more until the trees could start being unwieldy. Fast growing trees are fine for you! I like all the suggestions so far. My only recommendations would be to plant them in clumps, to your taste, and to include an evergreen/evergreen conifer or two for variety/ winter interest. Also try the tree forum for more recommendations.

Don't think of them as trees. What you need are very tall shrubs. That is why the Viburnum suggested seems like a good choice. You just prune them as a tree while they grow.

Viburnum prunifolium is not a shrub, it's a small tree--rarely tops 20 ft.

Shrub or tree is a matter of semantics regarding V. prunifolium. Based on the photo you provided it is a good recommendation from laceyvail and will also provide outstanding fall color. As emmarene accurately states you can prune them as a tree, meaning limb them up from the bottom as you would a birch tree to expose the trunks.

You could also consider any of the following as a multi-stem or single stem selection:

Amelanchier laevis 'Autumn Brilliance', Syringa reticulata 'Ivory Silk', Stewartia koreana, or Crataegus viridis 'Winter King'. Check with a local nursery to make sure the plants cultural requirements are consistent with your soils and local physiology. Good luck.

K&D V. prunifolium is native to my property. They are a small tree--no limbing up is required. Nowhere, in the woods or in the open, do they grow as a shrub.

Hmm, Missourri Botanical Garden classifies it as a shrub too. However, your local providence may display tree like tendencies. I've noticed geographic growth differences in Eastern Red Cedar.

Phlox, Hostas, and an elephant ear bulb that gets stored inside during the winter in Illinois