First of all, clear you mind of the concept that a planning document should be to any extent pretty, organized, specific, or "finished". Worrying about these things is pointless. You're out to make a game, not a planning document. Don't lie to yourself. Don't worry about appearances at this point, either. You can work on the concept art of your characters another time-- the game design document is about behavior and how things act. Specific details are best left to work out during the actual development, where you can actually test if certain things work well or not.
Next, clear your mind of the notion that your planning document is a "document". Clear your mind of the stereotype you place on creating a "document" and what you try to achieve in doing so. Now, let's recreate your definition of a game design document: "A place to write down all my ideas and keep notes of things I should try".
Notice I said "try", not "do". A decision in a game should never be final. Not until the game is "done", and I mean it. Your goal is to make a good game, and at any given time a mechanics shift might make it necessary to rework other elements of the game. It's fine, it's usual. Get used to the mindset that no idea is cemented in once you write it down, it'll be a service to yourself.
In fact, I would specifically encourage you to keep "try" lists. If you have a mechanic you're hazy on, write down a list of your different ideas on how to approach it. All too often I made the mistake of trying to design the final idea first. Bad! Write ALL OF YOUR IDEAS DOWN. Use a deductive approach, and eliminate the approaches you dislike until you're left with your most favorable one. I've found that in the process of this testing, you'll sometimes even think of a totally new approach which you'll like and end up going with.
Finally, I'd like to share what I think is the most important idea of this post. Don't write your document top-to-bottom. Don't work out every little detail of a concept before moving onto another. Outline your whole game, and then get more specific. I'll repeat. Outline, and then get more specific. You do this so you can see a picture of your whole game as soon as possible, and design it with everything on the table in front of you. When you work on things by just going top-to-bottom(not referring to writing on the page, but in your approach to working out your ideas on paper) you tend to get all stuck up in designing one concept without considering the others. It then becomes easy to focus on a small, possibly insignificant, chunk of your game when you really should be paying attention to the game as a whole. I can't emphasize enough the importance of this point. This approach has become absolutely fundamental for me to get anything done.
Bringing everything together:
- Don't worry about style, neatness, or polish.
- Save the artwork for later
- Don't try to be super-specific. "Come on, don't sweat the details!" - Hades(Hercules • Disney)
- Leave working out the details to testing.
- Write all of your ideas down.
- Try all of your ideas before settling with something that's "final"
- Be open to reworking concepts as the rules of the game change
- Design your game as a whole, not "top-to-bottom".
Hope it helped!
If anyone else would like to share their approaches, please email it to me or post a link or something in the comments. I love this kind of stuff!