It all depends on what you want.
Do you want trees or plants that keep their leaves year round or will trees that loose their leaves in the winter be ok?
I saw where you have a 2 & 4 year old. Do want trees that will grow fast so they can learn to climb trees or may even have a tree house?
Do you want trees or vines that give you somethig back like fruit and nuts?
Do you know what climate zone you live in? It seems Springboro is just south of Dayton.
Let us know.
You indicated that you live in a neighborhood with no trees. The trees I'm recommending here give you several advantages. They are beautiful landscape trees. They grow fast and they give either nuts or fruit.
Pecan trees. They produce nuts in 5-7 years and are great if you like pecan pies or have friends that do. By the time they produce fruit, your kids will love climbing them and they can play under them until then. They will eventually reach 75' tall and almost that wide. They really enhance a property. If you plant two different varieties they will produce more and bigger nuts. They are wonderful to set a picnic table and BBQ under. I recommend the Colby Pecan and the Southern Giant Pecan.
If you like walnuts, they grow 30 to 40 feet tall. They bear nuts in 4 to 7 years. They are also good landscape trees. They will also bare more and bigger nuts if you plant two separate kinds. I recommend Lake English Walnut, and Stark® Kwik-Krop® Walnut. The Stark tree bears in 2-5 years and is sold by Stark Brothers nursey. (They have been in business since 1816.)
For landscape trees, there is the Wilson Mimosa Tree. Mimosas, also called silk trees, add elegance to a landscape with fine, graceful green leaves and clusters of dainty pink flowers throughout the summer. An easy-care tree, it is both drought resistant and fast growing. Mimosa flowers attract hummingbirds and butterflies!
The maple tree is also a very nice landscape tree. They grow around 50 feet tall. Their chief claim to fame is the colors their leaves turn in the fall. They are absolutely beautiful. If you get a sugar maple you could even make your own syrup. Wouldn't that be a conversation starter?
If you like fruit you could grow lots of different trees and fruit.
Cherry trees. They grow 25 to 30 feet tall. If you get semi-dwarf trees they grow 15 to 18 feet tall and about 15 feet wide. I love cherries. If you get different varities you will get more and larger fruit. I would recommend you go to Home Depot or something similar and see what they have. Then I would go to a good nursery in your area and ask them to recommend cherry varities. The main idea is to plant what you like to eat.
North Star is a pie cherry that has been around for decades. It only grows 8-10 feet tall, but has beautiful cherry blossoms in the spring.
As far as evergreen trees go, I would recommend cedar trees. You can cut branches and bring in a very nice fragrance from the branches at Christmas time. They look very good on a mantle. We had many cedar trees on our 26 acre lot. The kids and I would make it a family outing to go and cut down the prettiest cedar tree we could find and put it up in our home for our Christmas tree.The kids would all disappear throughout the property and then come back to the house so we could all them go out and decide which one we wanted for our Christmas tree. After we brought it back home we would all come in for a cup of hot chocolate. Then we would bring in the tree and set it up. The kids and I still reminise about that. If you planted 7 or 8 at the very back of your poperty, you could go out with your kids and cut one down each year. Just plant a new one when you cut an old one.
When you plant a tree, dig a $10 hole for a $5 tree. You will be very happy you dug the hole more than was required. I usually take and dig a hole large enough that a 32 gallon trash can will fit in the hole and not be seen from ground level. I take a bag of steer manure and pore it into the bottom and ix it 50/50 with dirt from the hole. Then I add about 6" of dirt and then I plant the tree with about a 33/33/33 mix of dirt from the hole compost and plantng mix. Also, NOW is the time to get and plant bareroot trees. Bareroot trees are much less expensive than potted trees. I think they also grow faster and quicker/better.
I hope that helps. Good luck to you and yours.