Every bud can become a shoot/branch. If you don't want branches where buds appear (like on the trunk close to the ground), just rub them off. If you've waited so long that they are now shoots that you don't want, remove them with your pruner. That's all there is to it.
Fruit trees are frequently grafted to roots of a different variety, or even a different species. The rootstock is chosen for tolerance of growing conditions that the desirable fruit-bearing plant doesn't cope well with on its own. Under some conditions the rootstock will send up shoots we call 'suckers'. You ought to also remove suckers as they appear.
These actions (in and of themselves) will not harm your tree, but pruning can infect your tree if the cutting tool is carrying a pathogen from their prior use on an infected tree. Since you often may not know that the other tree was infected, it is a good idea to always sterilize you cutting tools before using them on any given tree. If you know that your tree is infected and you are pruning to remove the infected tissue, it is a good idea to sterilize before/after every cut.
Isopropyl alcohol (70%) is good for this purpose and will not corrode your cutting tools. Household bleach works well for killing pathogens, but will corrode your tools. With knifes and scissors/pruners I find it convenient to wipe the cutting surfaces with a alcohol soaked paper towel (or some such). Saws I drench (pour alcohol onto the teeth).
