The military wasn't particularly interested in whether a soldier was married or not, so we don't ordinarily find anything about family. Unless a soldier died during the war and next of kin filed a claim during the war establishing family relationship and a right to any payment due the deceased soldier, we don't ever see that kind of information in military files.

I believe you're mistaken about pensions. Even if a soldier lived through the war, he still may have died before his wife and left her a widow. In either case, based on his honorable service, a veteran or his unremarried widow could file for a state pension.

As for what you might expect, in most cases, there are muster roll cards showing when and where a soldier enlisted, for how long, and whether he was present or absent when roll was taken. If he's absent, the roll usually explains why and for how long. There may also be records of pay, receipts for uniforms/clothing and equipment, hospital admissions (why and where), furloughs to go home, discharges from service, surrender, prisoner-of-war camp records and other types of information. If a soldier died in service, there are often claims for pay due him by next of kin, sometimes with county probate records. Records are incomplete because many Confederate records were lost or destroyed during and after the war.