It may well be overkill, and you should certainly look at other software such as ICA-AtoM (http://www.ica-atom.org), a nice open-source application specifically designed for "straight" archive work, as well as commercial software like PastPerfect, which is relatively inexpensive and widely used in historical societies.
That said, CA could probably work nicely for your project. You may want to try it out and see how it goes. Worst case is in exchange for some time you learn more about how to execute your project.
In terms of hosting, GoDaddy is probably not going to work. They impose many limits on their hosting offerings, and in my limited experience with them performance of just about anything (not just CA) was abysmal. You might want to check out this page for some alternatives: http://wiki.collectiveaccess.org/index.php?title=Installing_on_Cheap_Shared_Servers
seth