The mechanics of the test are here
How Spatial Autocorrelation (Global Moran's I) works—Help | ArcGIS for Desktop
the conceptualization
Modeling spatial relationships—Help | ArcGIS for Desktop
requires you have some sense about the possible origins of the pattern, and the type of data (points, areas etc).
Since you should have some sense about what is going on in terms of the fossil locations, then the choice is yours. Do you feel that the finds are in someway clustered in space or purely random? If looking at distance, would it be inverse distance, or simple distance.
Basically... you can run the test more than once, using different scenarios... the task then becomes yours to interpret any findings in terms of the conceptualization. My guess (purely random) is that you would get clusters of fossils representing some unknown process (maybe cluster and die). This is counter to another process where the spatial pattern is purely random. Report back as to what you found and discuss it with respect to your 'hunch' about what went on.
