Julie is nice in that it's precocious and is decent tasting. But -- it's one of the most difficult mangoes to keep healthy in a container past a 3 gallon size. It has anthracnose issues, can't tolerate too much water, is sensitive to fertilizer, needs constant micronutrient applications, etc, etc. They are finicky little trees.
I'm surprised no one has mentioned pickering. It's super easy to grow, great tasting, and as precocious as the Julie (can carry fruit to maturity in a 3 gal pot). It's also small.
Jeff