Where would be a good place to search for a photo?
I once wrote a piece on finding photos of ancestors for Ancestry Magazine, back when there was an Ancestry magazine, but it didn't deal specifically with Confederate vets or Civil War.
General suggestions:
Google the name and look at Google Images. Add place and or dates to help narrow the search down if you don't find him right away.
Search Google Books. If there's an online regimental history and he was an officer, there may be a photo of him in there. Ditto if they have magazines like "Confederate Veteran" -- there might be a photo. (Or, look for a hard copy of the regimental history, since it would be cool to own one. I recommend Alibris or Abebooks, but there's always Ebay)
Search Ancestry - a lot of people post pictures of their ancestors there, and you may be descended from the same person.
Look on Deadfred.com - a place to post ancestor's photos. The odds are much smaller there, but you never know.
If you have an Ancestry account, look for photos on passport applications after 1914. You MIGHT also be able to find passport apps for free on FamilySearch, but I'm not sure. I don't know how likely you are to find a Civil War vet applying for a passport post-1914, but you never know!
If you do DNA testing, email your matches on that line and ask if they own any pictures.
Look on Ebay (seriously, I found my great grandfather's glass negatives on there!).
Go to Chronicling America - the Library of Congress's online newspaper database. Search for your ancestor's name and home state. The papers start running illustrations around the 1890s. Even if you don't find a photo, you may find an obit, interview, or other accounting.
Hope this helps!
Good Luck!