I usually sprout seedlings in a 1 gallon, or one of the 1 gallon treepots if available from my pot inventory. They seem ok to live in it for 6 months if it's a slow grower, or about 3-4 months if it's a vigorous one. Had a really large Valencia pride seedling that went a year in a 1 gallon and was strong and tall.
When I step them up, I go to a 5 gallon pot and hope to heck that they are well rooted, which my most recent batch really was.
Lately I use citrus soil with lots of sand, perlite, or pumice if I have it around. They seem to appreciate good drainage. I often put a layer of thick perlite or pumice directly at the bottom of the pot to encourage fast draining.
I have a few that went from 5 gallon to 15 gallon this year, but they are sort of stunted at the moment, the new growth keeps getting roasted off. This seems to be the make or break time for seedlings.
My largest mango, a diamond, is in a 25 gallon pot and is doing very well. Just finished top working it with peach cobbler, NDM, and sweet tart. It seems possible for it to live in the 25 gallon indefinitely.