Josh,
You're right, in a fight you don't want to go down to the ground on purpose. However, it's good to train grappling in case it winds up there! (Also, training will help you not wind up there).
In terms of positions, there are some who like a positional paradigm (a la BJJ or Judo, perhaps even wrestling) and some who prefer not to think in terms of positions (catchwrestlers, many JJJ, some Sambo, the ROSS crowd...).
I use the positional paradigm of BJJ. The reason for this is that position, as they use them, allows you to affect a lock, choke, strike, or other submission with less effort, because you use space and weight to your advantage. When you are not in a dominant position and you attempt a submission, it can be done--but it will usually require more strength or explosiveness than your opponent.
In terms of the heirarchy of positions, you will not hear the same scheme from more than one person. Some people think the guard position (on your back, with the opponent between your legs) is a dominant position. Others think it is a neutral position. Some call it slightly dominant. I think it just depends on the skill level of the parties involved.
In BJJ, the main positions you will hear about are the Mount, Side Mount (or Cross Body), Back Mount, and the Closed Guard. There are others, including 3/4, North & South, Knee on Belly, 1-leg mount, Turtle top & Bottom, and about a dozen variations of the guard. There are also minor control positions contained within the mechanics of each submission. These are more advanced, and are used to set up a submission or transition prior to finishing.
Best,
~TT