Dwilma01,
The United States Military did have military organization as well as military staff. Mainly pattered by the French Army's way of doing things as well as English and German influences. The amount of staff though wasn't as large as today's however, they maintain the basics of what the first Military organization called for in Colonial times. The Army during the Civil War wasn't large at all. Thus, the staff was limited in numbers but, with the inflation of numbers, staff to handle the administration aspects had to grow also.
Staff is an umbrella term. Let me write from The 1862 Army Officer's Pocket Companion - A Manual for Staff Officers in the Field
Article 18
Staff of the United States Army
There is in this army no corps identical in function with the Staff Corps of the French Army, which have been pointed out above (Art. 17)(excerpt due to space)
Colonel Scott, in his Military Dictionary, remarks, that the staff of an army may be properly distinguised under three heads.
1. The general staff - consisting of adjutant-general and assistant adjutant-general, aides-de-camp, inspector general, and assistant inspector general. The functions of these officers consist not merely in distributing the orders of commanding generals, but also in regulating camps, directing the march of columns, and furnishing to the commanding general all the necessary details for the excercise of his authority. Their duties emprace the whole range of the service of the troops, and they are hence properly styled general staff officers.
2. Staff-corps - of staff departments. These are special corps departments, whose duties are confined to distinct branches of the service. The engineers corps and topographical engineers are such staff-corps. The ordnance, quarter-masters, subsistence, medical and pay departments are such staff departments.
3. Regimental staff embraces regimental officers and non-commissioned officers charged with functions, within their respective regiments, assimilated to the duties of adjutant-generals, quarter-masters, and commissaries. Each regiment should have a regimental adjutant and a regimental quarter-master.
The military 'regulations' have always provided for staff position in the Army.
What isn't often explained are what goes on past the officers in the position of 'staff corps.' There were many lower ranking officers who did clerical work and still had a musket handy if they were required but--as a last resort. Couriers or "orderlies"--to whom memorized the orders as well as carrying the copy of it.
As to the first paragraph, I think the two top picks for staff would be Grant's and Lee's staff officers. Regimental staff stayed with their regiment so, this really depended on how the general staff and staff corps worked with new as well as old regimental staffers. Even so, the decisions made still rested on the general / officer in command, in my opinion.
Not much focus on staff was made during the war--they were often in support of the general though. With post Civil War studies, those officers who surrounded the top leaders from both sides seemingly won the spotlight. However, it would be most unfair, in my opinion, to judge a general's staff corps based on his popularity and or placement in the levels of 'fame.' Such as James Longstreet, "Stonewall" Jackson, Robert E. Lee, U.S. Grant, Meade, Hancock, Chamberlain, Griffin, Miles, Warren, McPherson, Rosecrans, Jno Buford, Sherman, Sheridan and this isn't counting those battle theaters in the west and so forth.
Just some thoughts and opinions.
M. E. Wolf