You may want to try something easier than a tropical. Most standard deciduous fruit trees, assuming you get the correct varieties, will grow here -- apples and peaches especially.
I have several persimmons and they grow well, as long as they get afternoon shade. Asian pears, particularly shinseiki and 20th century, will grow well here as well.

Mangoes, lychee, and longan will freeze to the ground in the winter with a good frost if not extensively protected. Definitely not for the beginning or carefree gardener. Some other tropicals do poorly here due to the salinity of our water.

You may want to try Baker's Nursery in Arcadia. I've also seen Fuyu Persimmon and 20th Century at the Walmart near my house off of Raintree and the 101.

You may want to also consider pomegranates and figs. Both are tough plants and do well here with minimal maintenance or spraying.

I have apples, peaches, nectarines, pears, Asian pears, apricot, plums, figs and fruiting mulberry all growing in full sun.

Currently I have santa rosa plum, pomegranate, figs, peaches (florida prince and tropic snow), oranges, white sapote, guava, and mango all growing in full day sun or all afternoon sun and they are doing great. The peaches and sapotes do need to be protected for the first couple of years, but once they fill out enough to protect the trunk they love the full sun. The pomegranate or fig is probably the best choice for around here. Low maintenance and very hardy in our soil. Of course grapes and passion fruit love the sun also but not really a tree. I also have 5 different avacado trees but I have them planted under the canopies of larger trees to protect them from sunburn and the low winter temps. I don't usually cover anything but the mangos and guavas on the coldest winter nights. The guavas actually survived uncovered on our coldest night of the 2010, 2011 winter(about 15 degrees)and they came right back in the spring. They actually fruited that year also which was quite a surprise. I am however done with the ficus natida as I had three 15' trees killed on that night. I'm in south Chandler and just don't have the micro climate yet to support these large trees over the winter without covering.

I have Longan, lychee, and mango if needed. 602-434-5641