Mr. Wise,
There were no dedicated, what we call today, Combat Support or Combat Service Support units during the War Between the States. There were officers and soldiers that held the positions from the Regimental level to Brigade to Division to Corps to Army up to the national level of the various CS/ CSS categories at the time (Ordnance, Quartermaster, Subsistence, Engineer, Signal, Medical). These men were within the units (usually an officer and a NCO) at each level and men were detailed (farriers, teamsters, wagonmasters, cooks, carpenters, provost guards, pioneers) to them to perform specific tasks. Below is an example:
Regimental level: Assistant Quartermaster (Rank of Lieutenant), Quartermaster Sergeant. Ordnance Sergeant. Commissary Sergeant. Surgeon, Sr. Assistant Surgeon, Jr. Assistant Surgeon, Hospital Steward.
You will find the records of individuals initially in the Compiled Military Service Records (CMSR) of their regiments and then in the CMSR's in the General Officers, Staff Officers, and NCO's CMSR's are separate from the regiments.
You can find a lot of information on issues, discussion, and other information on task organization, procurement, etc. in the Official Records (commonly called the O.R.).
The National Archives has a ton of correspondence to and from "national level" and I give some of this below.
Confederate War Department Collection of Confederate Records (Record Group 109).
109.7.2 Records of the Engineer Department
109.7.3 Records of the Quartermaster Department
109.7.4 Records of the Subsistence Department
109.7.5. Records of the Ordnance Department
109.8 Records of the Medical Department
Below are some sources you can look at that can give you a holistic viewpoint on supply, ordnance, medical, etc.
Risch, Ema. Quartermaster Support of the Army, A History of the Corps, 1775- 1939. Quartermaster Historian's Office, Office of the Quartermaster General, Washington, DC, 1962, pp. 333-468.
Sharpe, Henry G. "The Art of Supplying Armies in the Field as Exemplified During the Civil War," Journal of the Military Services Institution, JAN 1896, pp. 55-57, 61-64,73-80, 90,91.
Goff, Richard D. Confederate Supply. Duke University Press, 1969. Durham, NC.
Regulations for the Army of the Confederate States, 1863. Richmond, Virginia. Republished by the National Historical Society, Harrisburg, PA 1980.
Cunningham, H.H. Doctors in Gray: The Confederate Medical Service. Louisiana State University Press, 1986.
Hodge, Gerald D. Jr. "Sustaining the Army of Tennessee in the fall of 1863," Chattanooga Regional Historical Journal, Volume 5, Number 2, DEC 2002. pp. 195-213.
Please let me know if you have any questions.
Respectfully,
Gerald D. Hodge, Jr.
War Between the States Historian
Historian: 39th Georgia Volunteer Infantry Regiment
http://39thgavolinfrgt.homestead.com/39thHomepage.html