Re: How do you start designing a game?
First thing I do is I have a set of leisure activities that I partake on to help get the creative juices flowing, example taking a walk. Ones surrounds is a very good way to come up with a basic feeling or expression for the game, walking in a city as opposed to hiking will create several different ideas.
Once I have thought of a feeling I want the player to experience, I begin brainstorming specific ways to impose that feeling on the player. Take basic emotions and think of all the several ways this emotion can be generated, not just situations but mechanics.
Mechanics are huge, once I have in my head the emotion I want the player to experience I brainstorm how this can be achieved in different genres of games and then onto a new way of conveying this through GAMEPLAY in each genre. I emphasize gameplay because in conceptual phase it is very easy to forget about that and essentially I craft a film instead of a game. At this point I am sure you will be able to scratch off several genres that do not fit the experience you want to craft.
From here it is simple, list of mechanics, how they interact with the overall game experience. Then I begin my design document work, this is when visuals become important in order to convey them clearly to the artist reading the document and the mechanics become more fleshed out to describe the system and amount of interaction with the environment and any objects in said environment for programmers sake.
Story and visuals for me all hammer home the experience or experiences you are trying to convey to the player, they can either reflect the mechanics or vice versa depending on the game you intend to create.