I would stay away from Julie and Ice Cream because they grow at a snails pace and can have disease issues. I know you said you said you are keeping it in a pot in a small yard but I would still recommend you grow a vigorous variety because Mangos grow relatively slow here in SoCal.
By growing a vigorous variety, your tree will be better able to outgrow disease issues which we normally encounter in Winter and early spring. If you purchase a grafted tree. It will flower in its first or second year and the extreme precocity will cause a self dwarfing effect.
I’ve had a Pickering mango on Florida Turpentine rootstock that was planted into the ground and it actually did ok and produced some fruit but even in ground, it grew very slow and was very droopy.
The droopiness is caused by the heavy flower panicles which form every Winter and this causes the branches to be exposed to the sunlight which in turn causes sunburn damage and an entry point for pathogens. This will happen regardless of what rootstocks it is on but if you planted a vigorous variety, you can prune away downward facing branches and keep the upward facing branches but with slower, dwarf or condo mangos. The growth rate of vigor may not allow for additional vegetative growths due to the inherent nature of slower growing varieties, especially in our climate.
Sweet Tart is a variety that I would recommend. It is considered vigorous in Florida but most grafted varieties grow much slower here compared to when grown in warmer climates. I recently posted pictures of my small sweet Tart trees grafted onto California rootstocks that are only about 12 inches tall and holding fruit.
I can see you being able to keep a grafted sweet Tart in a pot for several years, keeping it at around 3-4 feet tall and just as wide with little effort. It will take probably 2-3 years just to get your tree to this size but once it reaches this size, you can easily maintain it at that size and it should be productive because of its disease resistance.
At the size stated above, you should reasonably be able to expect about 1-10 fruit annually with probably 5 Fruit being a realistic average in year to year production. Sweet Tart has been reported as being alternate bearing so you may get few to zero fruit after a good year.
It is easy to stick a mango tree in a pot and call it good but if you want to maximize growth, have a healthier tree and start harvesting mangos sooner rather than later, I would recommend you root prune your tree and ensure you use a good quality soil that is fast draining.
I can’t emphasize enough how important it is for the health of your tree(especially when potted) to have a dense, heavily branched root structure that will anchor it better in the soil and to help your tree uptake more nutrients and water.
I could type a lot more info about this but Dr. Whitcombs video will save me a lot of typing.
https://m.youtube.com/watch?v=_lkDLSPWZd0Simon