I think it is best to learn both. Most people I know say you should always learn the formal first, because the informal comes easily usually as you learn! I play korean online games and usually people do talk formally to each other when they are strangers. It is impolite even in the games. But if they know you are a foreigner, they may let it go! Also, many will use korean slang online, so you might want to learn some of that eventually too! (:

Although I don't really know much about the online game world, this might help. I thought the informal speech might be preferred because it is shorter. But you mention talking to gamers you don't know, which suggests formal speech since that is how you talk to someone you first encounter. Whatever is the case, I think it is best to have an open mind and learn both from the start. Both types of speeches are very deeply ingrained in the language. It is really not easy to just concentrate on one of them. You might waste time trying to separate the two, since what you want to skip over will always be in your way one way or another. I would suggest you learn both. In the long run it will save you time, I think.