The current thinking is that you dig a hole only as deep as the root ball. You want the root flare to occur immediately above the soil surface*. Planting too deep is all too common and can ultimately cause the death of the tree. You cannot assume that trees were planted at the correct depth at the nursery, often they were not. In most circumstances you backfill only with the existing soil, no amendments. The width of the hole is kind of up to you so long as there is enough room for proper root spread. It helps to rough up the sides and bottom of the hole with something like a garden fork to reduce the shovel glaze/hard texture transition at the edges of the hole. For B & B plants you always remove as much of the cage and burlap as is feasible.
These days some people are completely bare rooting B&B or container wood plants to correct any root problems at planting. I don't have enough experience with this method to have an informed opinion save to say that it would be imperative to work quickly but carefully and keep the roots continuously moist. I can see both pros and cons to this method but I doubt many commercial landscape contractors will embrace it.
Much of the credit for current planting and pruning thinking goes to the late Dr. Alex Shigo who performed postmortem examinations on hundreds of trees in his long career to reconstruct their history of growth, disease, insect pests, abiotic injury, decay and compartmentalization.
* The soils you are planting in can dictate some variations on standard practice but generally it is better to plant slightly too high rather than too low.