I think that size is sufficient as a beginning point. Linguistically, you want your word to do one thing to keep things simple. Classify all items by size as asteroids or planets. Where they are, the type of orbit (or lack of one), what they are made of should be a qualifier. Otherwise you have to have a different word for a planet based on where you find it. Orbiting a star = planet, orbiting a planet=moon, beyond the Neptune or not having a clear neighborhood=more classifications and words than we can currently foresee. Yet, scientifically, they all have two common characteristics, shape due to size.
Once you want to add an additional characteristic, you should have new words that tell you about that specific characteristic. Ones in the inner solar system are solar planets, those out in the Kuiper belt or Oort cloud are Kuiper planets and Oort planets, and those out between the stars are interstellar planets. Likewise, an asteroid is an asteroid no matter where it is, and you can add any modifiers you need (asteroid moon or moonroid, solo, irregular, rouge or solar asteroid, belted asteroid, Kuiper asteroid, Oort asteroid, interstellar asteroid, etc.). If you want to talk about composition, then you have gas planets (giant ones if desired), rocky planets, ice planets, diamond planets, silicon, iron or any other crazy combination that comes up.
Then, no matter what, you can describe what something is so that most people can understand. Rocky interstellar planet v. rocky solar planet v. gas solar planet v solar belted asteroid v interstellar belted asteroid etc. Have each word do as little as possible, and add a couple of informative words that convey any additional information instead of combining and making thousands of words that try to do 3 things at a time, which implies needing 8 words to tell the story of things that are different on each of the three parts of the definition of a planet from the 2006 definition.