This doesn't address your question unfortunately, but the most recent Civil War Digital Digest episode is about regimental staff positions:
In all sincerity, a large part of staff work was probably about the relationship with the officer in question, much like an assistant to their boss today. Obviously competency is a factor, but people are going to select those they work well with even if it means learning on the job.
I think it also varied a lot general to general. Some samples:
View attachment 399758
General Ulysses S. Grant and Staff: Ely Samuel Parker (left sitting), Adam Badeau, General Grant (at table), Orville Elias Babcock, Horace Porter. c. 1865
Ely Samuel Parker - The two were friends from their time together in Galena before the war; no prior military experience
Adam Badeau - Recommended by John Rawlins to join the staff; was staff officer prior to selection
Orville Elias Babcock - Selected by Grant for his service as an engineer at Vicksburg
Horace Porter - Grant was impressed with Porter and selected him for his staff; experience from earlier in war
John A Rawlins - The two were friends from their time together in Galena before the war; no prior experience
View attachment 399759
McClellan and Staff; Portrait shows from left: Lieut. Williams, A.D.C., Surg. Walters, Brig. Gen. G. W. Morell, Lt. Col. A. V. Colburn, A.D.C., Maj. Gen. G. B. McClellan, Lt. Col. N. B. Switzer, Prince de Joinville, Comte de Paris as identified on the card mount. c. March 1862
TBH this photo is entitled McClellan and his staff but I'm not sure if that's accurate.
Lieutenant Seth Williams ADC - Met McClellan prior to the war, but had experience from Mexico as an aide-de-camp
Surgeon Walters - can't find any info, but he's a surgeon based on the caption
General G. W. Morell - went to military school; I don't think he was on McClellan's staff
Lt. Col. A. V. Colburn, ADC - extensive prior military experience
Lt. Col. N. B. Switzer - Couldn't find reason
Prince de Joinville, Comte de Paris - Political appointment
Since this is March 1862, here's more of his staff from Wikipedia (
https://en.wikipedia.org/wiki/Peninsula_campaign_Union_order_of_battle)
- Col Thomas M. Key - Chosen for skills
- Col Edward H. Wright - Appointed
- Col John J. Astor, Jr. - Couldn't find reason, but he belonged to a powerful family
- Ltc Albert V. Colburn - see above
- Ltc Nelson B. Sweitzer - see above
- Ltc Edward McK. Hudson - West Point grad, appointed
- Ltc Paul Von Radowitz - Son of Prussian War minister
- Maj Herbert Von Hammerstein - couldn't find reason
- Maj William W. Russell (USMC) - paymaster
- Maj Ferdinand Lecompte (Swiss Army Engineer) - observer
- Cpt George A. Custer - West Point grad
- Cpt Joseph Kirkland - couldn't find info
- Cpt Arthur McClellan - George's brother
- Cpt Louis Philippe d'Orleans - appointed
- Cpt Robert d'Orleans - appointed
- Cpt Martin T. McMahon - appointed
- Cpt William P. Mason, Jr. - couldn't find info
- Cpt William F. Biddle - couldn't find info
- Cpt Edward A. Raymond - couldn't find info
I'm not sure what "appointed" specifically means.
But there's a taste. This was just off of google so if anyone sees any errors or omissions please point them out.