Platform selection will influence decisions about site organization and design, among other things. You may or may not start out knowing what platform you want to use, or you may change your mind about the chosen platform based on the way you want to organize your exhibit, the way you want visitors to interact with it, and whether you want to have the object available in digital collection form as well.
Some considerations that should be made when considering platforms include:
Ease of use and customizability
Whether there needs to be a searchable collections component
Whether exhibits should be navigable linearly, non-linearly, or both
The types and level of interactivity desired
Accessibility for the disabled
Some common platform options:
Omeka (.net and .org) [accessibility statement]
Wordpress (.com and .org) [accessibility statement]
For more information, see Comparing Systems for Creating Digital Exhibits by Dr. Pamella Lach