I have worked on a couple pretty big
commercial theatre projects that draw heavily on archival sources so I have had to deal with this on a few different occasions. First of all, the biggest key is insuring you have a workflow and assetflow that keeps good tabs on content origins. We used a custom built FileMaker database on these projects to keep
track of rights clearence and images that we just found on the web would always have their webloc file kept in the same directory as them at all times. Most of the content we used wasn't cited since everything was either public domain and thus did not legally require a citation or was licenses from something like Getty, AP,
etc in which case no citation is required since we are paying for the rights and the license contract generally does not require that. A couple archival sources wanted a listing in the playbill and that was just listed as "Archival Media Sources: NBC, ..." in the back.
Additionally, I always insure that the producers take responsibility for all rights clearance issues. A couple weeks before the show goes into to tech I'll provide the producers with a document laying out everything that needs to be license and it is on them to make that happen. They can then come back and make me cut unlicensable content but at the end of the day I don't want to be the one who gets sued if something isn't cleared properly. I'm guessing you are working in a non-profit or educational context which makes things a little
bit easier since things like fair use can be applied a little more generously. In general though, I would say that you shouldn't worry about citing all the different sources since you either don't have to or you have to actually license stuff in which case the licensor will specify how they want it done.