I think that back yard growers have tons of options to choose from, just look at how many mango aficionados complain of not having enough room for that new variety.
Where I think breeding work needs to be done is in commercial varieties. the pickings are slim in this area.
What's needed?
* A fruit that can be picked mature green, but ripen perfectly, after 2 weeks.
* Firm and thick skinned to for shipping.
* looks nice , ( colors sell, think of those poor souls that mistakenly select the beautiful Tommy Atkins over a greenish yellow Kiett )
* Disease resistant
* Productive, and reliable. ( Not so dependent on climate triggers to know when to flower )
* Smaller tree, good for high density farms, and easy harvesting.
* Taste like a top tier mango
* 100% fiberless with dark orange flesh
So if I had to select which fruit to get traits from.
Kiett : for its productivity, disease resistance, shelf life and shipping ability. but lacks color and quality of fruit (flavor and texture ) can be improved on.
Tommy Atkins: for all it's commercial traits, and color.
once you have this you "pair" it with something that will improve the fruit quality.
many of the top tier mangoes , seem to be very finicky into picking times or that narrow window of perfect ripeness. for someone that has a tree in their back yard, this is not much of a problem, but having fruit that has a longer shelf life is an attractive trait even for backyard growers.
for home growers, I think the following traits should be focused on by breeders:
* Disease resistance
* Consistency in quality and production each year ( not so sensitive to climate such as, for example Glenn, Angie etc )
* Naturally dwarf
* Long shelf life and forgiving in when you pick them.