I live 20 miles southeast of new orleans louisiana

apple trees don't get very tall, and are actually more productive if you keep their tops trimmed low so they tend to branch outward. Also makes it easier to get to the apples.

Crepe myrtles are attractive flowering trees that are a good size for home landscapes. The multi-trunk aspect is very pleasing. The bark on the trunks is smooth with attractive colors. They come in a good assortment of flower colors in shades of light pink to red, white, and various shades of lavender and purple. They would fit well in your size limit.
Wax myrtles, Ligustrums, and Cattleya guavas are also used in this size category in Florida. Crepe Myrtles work in a wider range of climates.

In your area, you could probably grow an orange or lemon or lime tree, they stay fairly small. Another alternative is planting a crepe myrtle and trimming it into a tree shape instead of bush style, would not kill out your grass as much since there is little shade.

Ilove Red Buds they only get about 15' tall and they flower in the spring and the leaves are heart shape.

Flowering crabapples are good, just make sure you get one that doesnt grow very tall, there are a lot of pretty ones as well as weeping ones. You can find some Japanese maples that are gorgeous, and some don't get more than 15 or 20 feet. Be sure and check the tags. Dogwoods are beautiful, so are the tulip and star magnolias. Redbuds, (and whitebuds), I am assuming you can grow them there.