I haven't played the game before but from what I have read on the forums here, I have gathered that there are different size planets and they are numbered accordingly. Example a category 1 planet would be near worthless while a category 15 planet would be a rare special find. What differs between the two are buildable squares. Buildable squares are squares that can be inhabited with your buildings and factories. Each planet is limited to a certain number of them. The planets also come with inhierent bonuses.
So to answer your question... planets are measured by the number of buildable tiles.

Actually, Earth is used as an "Average" planet classification from what I've seen. Every game I've played has had Earth (without picking the bonus to starting planet) at a class 10, pretty middle of the road for what you see in the Universe. In terms of the range, I've seen planets from 0 up to 24 (the theoretical limit is 26, but I haven't seen one yet)

Earth is a medium-ish planet and without the picking the home planet bonus, it's not the best starting point in a sandbox game, and Mars has always been a class 4 or 5 in my games so your starting system as Human is pretty limited.

There are reasons to take a low class world.

Political - Small planets have small populations that just love you. Many small planets can help you carry an election (when you run the democratic governments).
Cultural - Small planets are still your planets. This means they help extend your cultural reach across the galaxy. Useful when you are trying for a Culture win.
Military - A simple fuel depot, extending the range your starships can travel.

Their are a few different terrain looks, and small planets tend to have that "Mars" tile set.

At the moment, the smallest colonizable world is PQ 4. The smallest levels (1, 2, and 3) have been "turned off".