Hi there!
In Sicily you can grow a lot of subtropicals tree, but i fear, not any true tropical tree (I mean coconut, durians, mangostan and stuff like that). Regarding mangoes, they probably will do fine in your place, but they are a relatively new culture in the island, so you won't find any fancy variety: you, however, won't find any problem in adding kensington pride, kent, keitt, osteen, maya, tommy atkins, irwin, glenn mangoes to yor collection, they can be found in nurseries on the island. Maybe some other nursery in europe has a richer selection, but yet, you won't find any of the newer Floridan varieties. Regarding avocados, even for those the selection is limited but you can find at least he main clones. Jackfruits: anecdotal experiences show me that they can grow, they can fruit, but the season is too short to have them ripened. You can use them as vegetable. Breadfruit is out of discussion. Litchis grow well if you provide them a wind break. Cherimoya and atemoya grow aswell; i'm unaware about other annonas. Papaya, you have to cover them for the winter, won't survive outdoors unless in the hottest location. Longan, casimiroa, passiflora grow well. Macadamia and pecan grow well aswell. Sugarcane do grow. Bananas: you can grow all the most cold resistant varieties; You can't hope for good results with an Ae'Ae or Veinte Cohol but you will fruit without any problem A Namwah, an Orinoco (fun fact: the Orinoco are actually endemic in Sicily and some people assume they have been introduced by Arabs), Brazilian, Goldfinger, Sweetheart (you get the idea): you can find pretty much every banana available to the American market. Loquat do exists in varieties that are unavailable to anyone else in the world.
The strong point of Sicily are, of course, the citrus. Even if the Sicily is home of the best among the blood oranges, you don't have your property in a zone were blood oranges do the best results. Still you will have the possibility to get some interesting stuff that is unavailable to USA members. The most common stuff shouldn't be grown: you will find more oranges grown from your neighbors than you can possibly buy/eat. Focus on the rare/hard to find/traditional stuff. Whatever happens, don't introduce any bud wood from outside the EU. Aside the fact that is useless with all the diversity of citrus you can find in europe, potentially it can create big issues.
Don't forget that cold winter are also an advantage, so you can grow also a lot of temperate fruits. Persimmon, figs, carob, pomegranates, apricots, almonds, peaches, and the list goes on. Palms will grow but they will be obliterated in few years by the red weevil.
Your main issue will be the lack of documentation from other people, the lack of specific books talking about the growth of tropical and subtropical fruits in Sicily and the lack of programs like the citrus protection programs. But with patience you can overcome all of those.
PS: plant some grapes!