It should automatically stop whenever a msg that needs your attention arrives. If it skips over even when a message is received, it means it doesn't matter and you can totally ignore it. There is a setting to make it skip every msg, so if that is happening, maybe that setting was somehow changed in your game.
All the msgs do come in the order that is written in the guide, but only if you reply with the right response at the right time. For example, if you receive msg A and reply back, you will get msg B, but if you don't reply back, you might get msg C or D and miss an important plot line.
Steins;Gate is not an easy game to understand and play because it's so different from other J adventure games out there, but once you understand it, you will be able to get 1000 in no time.