Map Enthusiasts

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.

EDIT: To be clear, i know about projections already. I'm not worried about picking a projection. What i'm asking about is the process is for taking a physical globe and projecting that globe's surface onto a flat rectangle. I don't know how to turn an imaginary cylinder or cone sitting on my globe into a tangible physical or digital map. I don't have the means to cut up and unfold my globe until it's flat. What is the actual process for making a map from a globe, for any projection? I know this isn't how maps are traditionally made, but surely there must be a good way to do this.