I have a clear globe that i would like to project to a flat map. Any common projection should work, since computer programs exist for converting map projections. Where should i start?

A couple of details: First, my “globe” is an empty plastic Christmas tree ornament, so it can be hung from a string at one end but it doesn’t have a stand like a normal globe does.

Second, this is a worldbuilding thing. My globe does not represent any real planet or similar body, which is why i need to make a new map from the globe instead of finding an existing one.