I am about to bring the wrath of all the mango snobs down upon me, but I would go with...
Nam Doc Mai
One tree but fruit can be used at all stages of development for different purposes. Don't get me wrong, I like complex mangos. But if I can only have one, I'm going with the one that can be used green like an apple but still tastes good ripe. It is the Swiss Army Knife of mangos. Yes, there are better green mangos and mangoes that are better ripe, but if I only get one I am going with the one that does everything reasonably well.