Lemons and Oranges or whats popular but the problem with this is that when your oranges start fruiting the cost in the supermarket for the same orange is often super cheap and fresh. Because they are so popular the pests of this tree are popular. eg. Gall wasps are often controlled by industrial methods but the home gardeners tree gets attacked and they don't have the resources to out power these pests. Basically if the fruit in your backyard is the same as the one you easily buy every day of the year anyway you are only exposing yourself to 1% of what fruit has to offer you.
So why not choose something like a Mulberry Tree, Black Sapote, Pecan, Sapodilla, Miracle Fruit, Peanut Butter Fruit, Lychee, Soursop, Custard Apple. And when you do choose a variety choose a variety that isn't common to your supermarket. Eg. If you are going to get an Orange tree then grow the Navelina. After you eat this variety you will wonder if they really are selling oranges in the supermarket the taste is so different.
Mistake 2: You are a Cheapskate
A seedling tree might cost $10 but the same tree as a grafted variety can cost upwards of $35. So people choose the seedling and then get disappointed why it doesn't fruit. A grafted tree can fruit often 3 years before a seedling even thinks about bearing fruit plus the fruit being produced is a proven quality and taste. Obvious example is that you eat an orange, love it and then plant the seed. 8 years later that seed produces its first "oranges" and instead of tasting sweet and having orange skin, it has a very light yellow skin and is almost un-edible. Same goes for Lychees, Apples, Pecans, Macadamias etc etc.Mistake 3: You Plant it "Wherever"
Fruit trees love the sun and they love good drainage. Pay attention to the way the sun falls on your backyard throughout the year, especially in Spring and then make sure you use that space for your fruit trees. Your shady spots are perfect for rainforest trees, so don't let them go to waist.