For most of my life, I assumed that I couldn't be descended from slave owners. The parts of my family I know the most specific details about came to America after the Civil War, or immigrated before the war to Union states where slavery would have been outlawed long before they arrived. But there are some parts of my family that did live in the South during slavery. I'd always assumed that they were poor subsistence farmers who wouldn't have owned slaves. But I don't know this for a fact.
It should be fairly easy for me to find out the names of people in that part of the family who were alive and of age at least during and just after the Civil War. My grandmother on that side is alive, in her 80s, and mentally sharp as a tack. I also know fairly specifically where these folks lived back then. I'm dimly aware that I have one ancestor who briefly fought for the Confederacy, though we've never been able to find any documentation about this.
What are the best resources for this type of research? Are there public documents that would include wills or details of ordinary non-wealthy people's estates? Would information about slaves changing hands be published in newspapers of the day? The people I'm thinking of definitely were not socially prominent or public figures or anything like that.
I'd second what u/captainkickass said. I'd also recommend getting an Ancestry.com account. One thing I've learned from having it several years is that many times people have already done your work for you. As you find names, dates, etc. you also have full access to almost all census records, as well as slave schedules. Wills in particular are helpful, and many times people have found those and scanned them in. Its how I actually found an ancestor owned a slave. Information about slaves changing hands would be very hard to find, as most of that would not be published, and even if it was, you'd already need to know the exact date and place to begin looking at old newspapers to find it.
For the ancestor you believe fought with the Confederacy, I'd look first at https://www.nps.gov/civilwar/soldiers-and-sailors-database.htm. You can find muster rolls that may correspond to your ancestor. Bear in mind, though, if the name is not all that unique (there are thousands of James Smiths in the Civil War) you may not be able to narrow it exactly.
As an aside, don't just go into this to look for slave-holders. Regardless of whether or not you answer that question, there is so much information you may be overlooking by focusing on that one aspect. If you find a will, see what other items they placed value in. Check census records in different decades and see if family members died or they had boarders living with them. Look at occupations, the way names are spelled, etc. Just looking into your own history, no matter what you find, can be very rewarding.
Start with your grandmother. Talk with her and record your conversations. Ask any question you can think of, then ask it again later. Take notes.
Start looking at census records. Ask for as many family records you can get your hands on. Bibles, birth/death/marriage certificates, pictures, documents, etc.
Then it’s a matter of tracking people backwards and finding more records. Message me if you want help.
UPDATE: A few hours with a free trial of Ancestry.com produced a trail that dried up pretty quickly. As of the 1860 census, all of my Louisiana ancestors were illiterate monolingual French-speaking subsistence farmers in Lafourche and Terrebonne parishes who, at least per the census, did not own slaves. That leaves a window of time in the 18th and early-to-mid 19th centuries where someone may have had a level of affluence I'm not seeing evidence of, but it seems unlikely. My guess is that most of these people did not have wills, but I'd be curious to know how property and estates were handled in a largely illiterate population who often didn't speak the language when it came to American courts of law.
I did get clarity on my Confederate ancestor, who might not actually be related to me at all. He had a very common name, and the only available details are sketchy and don't correspond well to other information I could find.