Video is good. I got to thinking about this question and thinking back to when I was younger. Some of the museums that stick out the most to me were places that had these little movies you sat through before you went through. Or which were maybe a part of a display in the museum. Others that stick out were places where they did living history and had folks dressed up in period clothing and maybe acting as if they were from the period. You say this is a mid-sized museum so I doubt you could afford to pay someone to come in every day and dress up just to interact with the visitors and be able to answer their questions. But you might be able to do the video. Try contacting some local re-enactors and see if any of them would be willing to film the video. Have them look over the items in your collection and pick out a few to discuss. Then do like a ten or fifteen minute video as an introduction to the exhibt. In addition to that ask them if they might be willing to write detailed descriptions about the items in the exhibt, especially the ones not picked out for the video.
You may still have to pay the re-enactors for this service, or maybe they would be willing to do it for free. But depending on how you work things out that may be a one time fee. And as re-enactors spend more time studying the period they should be able to help folks understand what things were like during the war.
Another thought would be to try and find some letters or journals from the period that somehow tie in with the item in question. Maybe one of the items was was used at the Bloody Angle during the Battle of Spotsylvania and there's a letter or diary entry from a soldier describing the fighting there. Or maybe you can get something from the soldiers or civilians that talks about using a particular item. In the Weapons thread we got to discussing sharpshooters and the some of the rifles used. On page three of that thread (http://www.civilwarinteractive.com/forums/forum27/234-3.html) I mentioned that Philip Katcher's The Complete Civil War had something that could be described as the use of a sniper team at Port Hudson. And the sharpshooter was using an Enfield rifle (it's on page 223 for anyone who wants to read it). Perhaps one of the items on display is an Enfield rifle that was used by the sharpshoorters, there you have someone actually discussing seeing an Enfield in use which maybe you would print that action for vistors to read.
If you have artifacts I would explore the lives of the soldiers or civilians who owned them. The story of the war is much more interesting if it is told through the people who lived though it. And I mean more than their names, what they did, what their other experiences would have been.
If you have an artifact, telling the story of those who made it and what their lives were like would also help.
As a CW buff, its detail that is important. I am not so interested in an artifact as I am in what it can tell me...