When selecting a didjeridoo to have and use as a musical instrument there are a few things to keep in mind:
The most important thing to ensure is that the didjeridoo is completely hollow. The fact that there appears to be a hollow at either end is not evidence enough. You should be able to see light clearly as you hold one end to an eye. No matter how chiselled out the end may be, if the centre isn't hollow it will not play.
Holes and cracks in the body of the Gunbarrk are also worth looking for. As the Gunbarrk is a living thing, it will expand and contract with climatic changes. Small cracks in the surface are not generally a problem. Any cracks can be checked by placing the lips over the crack and sucking. If air comes through it needs sealing.
Acrylic paintings tend to seal the didjeridoo and sound whereas the life expectancy of an ochre painting on a didjeridoo is controlled by the amount of fixative used and the amount of wear and tear it is exposed to.
Size is more an individual choice. The total inside diameter is what determines the quality of sound produced. Thus, bigger diameters in the hollow usually indicate a deeper, fuller resonance.
Another thing to look out for is that the mouth piece seals the mouth. Playing with the instrument to the front or side of the mouth is an individual decision. The important thing is to have the mouth sealed, so it is airtight. A wax mouthpiece aides in this and makes it more comfortable for playing over long periods.