You'll never go from being a private to a commander since those are two different services. You'll probably never go from being enlisted to being a commissioned officer unless there is a long war that kills lots of active officers and new ones can't be trained fast enough.
edit: I'm not sure about your army, but in the Canadian forces, Commander is a naval rank, equivalent to Lieutenant-Colonel in the army. Captain in the navy is equivalent to Colonel in the army, and Lieutenant in the navy is equivalent to an army Captain.
Navy: midshipman -> acting sub-lieutenant -> sub-lieutenant -> lieutenant -> lieutenant-commander -> commander -> captain -> commodore -> rear-admiral -> vice-admiral -> admiral
Army: officer cadet -> 2nd lieutenant -> lieutenant -> captain -> major -> lieutenant colonel -> colonel -> brigadier -> major general -> lieutenant general -> general
So in my program, I would have had to train as an officer cadet for four years while I earned my degree. At that point I would be commissioned as a second lieutenant. Then I would imagine it would take something like four or five years to progress through lieutenant to captain (the army version, or air force in my case), but I didn't stay long enough to find out.
hope that was useful.