They should just ask some real world astrophysicists to work on some proper, consistent classifications based on our current planet hunting.
Currently I assume that we would need differing classifications for:
Planets, Planetoids/dwarf planets, asteroids, and satelites.
We'd need gas giants, rocky planets, and ice planets with or without rings.
We'd need geologically active or inactive, strong or weak magnetic field.
We'd need atmospheric composition, atmospheric pressure, and temperature/temperature extremes.
We'd need life or lifeless.
I bet plenty of scientists would work on the classifications for free!
That gives us a fair range of possibilities with enough scope to cover our list. They need to get to grips with a logical progression though. Class M sits in the middle so what should be either side of it? It would make more sense to me if they started with rocky, then gas, then ice with variations on the scale.
So Class A would be very hot, rocky, low atmosphere, low magnetic field, tidally locked, lifeless, close to a star - like Mercury.
Class B would be gas giant, hot, low atmospheric pressure, low magnetic field, tidally locked, lifeless, close to a star.
Class C would be gas giant, hot, high atmospheric pressure, low magnetic field, tidally locked, lifeless, close to a star and so on.
I suppose they could also adjust classification depending on whether a ship could safely pass through the atmosphere.