The feeling that the character is supposed to portray is important. If the character is supposed to be a terrifying enemy there's not much point making it with soft, round edges and about waist high. For multiplayer models for games such as Half-Life Deathmatch or Quake 3 Arena, there isn't a great need for continuity between the model and its surroundings. However, you should still try to keep the theme throughout the character, i.e. same style of clothes as its hairdo etc. After you have a basic idea in your head its time to put pencil to paper.
Concept art is vital to the completion of a project.
If you do a good set of concept drawings and stop work on the project for a while, you can come back and pick up where you left off. When first drawing a model you should draw the basic model in one go. Once you are happy with the design, you can to draw the model in many different poses and positions, this way you will get a feel for the character and create a personality for it. You will probably need to modify them to fit the limitations of the game engine. Every game has its limitations, knowing these limits can make a good model a great one.