Video is extremely valuable. For goalkeepers, video is going to tell a lot about quickness and also game decisions. Do NOT submit a full game, especially for goalkeepers. I certainly can see why a coach would request a full game for basketball. Since only five play, it is possible to see a lot about a player off the ball, defensive abilities, how much playing time the player gets, the whole nine yards. For a goalkeeper, who may get only so many plays a game, well, I do not see a coach doing more than ignoring the video entirely. I would keep the length to five or six minutes.
I do disagree with @ISDN1200 about when to start. Start now. I had one coach (boys) tell me that he was grateful for more than one video (a year apart) because it showed development.
I would shoot at least four games, more if possible. If the only reason you are shooting is your child and he or she is a goalkeeper (and there are other possible reasons, like highlights for a team banquet), focus the camera with a decent view to capture a good part of the field in front of the goal and leave it there. Make sure that the camera view is wide enough to see the keeper coming off his or her line. And situate it somewhere where the coaches and bench players will not block the view. As your skill level increases, you can try zooming in, but you always run the risk of missing a part of the play and it can be distracting.
Editing software doesn’t need to be that fancy. I think I used IMovie. Just divide the tape up into skills from the several games. Start with saves. Then do coming off line, punts, six kicks, corners, crosses, one on ones.
I do believe that it is possible (at least at the D3 level) to be recruited based on video alone. This is even more likely to happen at the margins with goalkeepers, since it is a specialty position. If a team needs a goalkeeper, and has three in mind and all three commit elsewhere, it is possible that the decision would be made on video alone. I doubt however, that any coach would recruit a goalkeeper without either seeing him or her in person or on tape.