The answer really depends upon the type of tree. Some trees sucker on the bottom, and it's not a problem. Some are grafted, and if they sucker on the bottom, it's likely the root stock suckering (this should be trimmed off).
It also depends on your location. In really hot areas, suckering can be the plant's way to shade itself from the heat. Eliminating the shade could cause the stem to burn.
As for the stake, to properly plant a sapling, if the plant is too flimsy to support itself, you should have three stakes forming a triangle. This allows the plant to move within a narrow area. Movement is required for the plant to build up good strength. If you leave it staked like that, there is no flexing, and the plant is weaker than if it is allowed to bend.
Just make sure the amount of motion allowed does not cause the roots to move around, or they won't get established. Speaking of the roots, you should always spread out the roots and inspect for girdling roots when planting a tree from a pot. Circling roots is very common in potted trees, and if not corrected, your tree is very likely to have stunted growth or even die from strangling itself.