I've never used balsa as a core material, however I'm very familiar with balsa from other hobbies.  I'm thinking it may be my best bet as a core that needs to be shaped. I know I'll have to drill it.  What else do I need to know that is different from a cloth or honeycomb based core?

Depends what you mean by needing to be shaped. Do you mean being able to form a sheet over a curve, or sand/grind it to form an unusual shape? I've only used it from half inch upwards, and not sure if it comes much thinner, but as the king said, it normally comes in sheets of end grain blocks glued together with a scrim on one side. So the sheet will bend one way, but not the other, and when it does bend you're left with loads of gaps between the blocks that will need to be filled with thickened epoxy.