TEVIN is right in that you're a bit vague on whether or not you want opinions or official details, as there are no official details on sequels. However, if you want opinion, I can give you that.
At the very least, one sequel. Why? Because the concept of a 'trilogy' has been done to death and the last thing this franchise needs is for something so boring as the idea of a trilogy to weigh it down. So at the least we need one sequel if the movie does well enough to warrant one, but I will never say that exactly two sequels will ever be warranted. If this movie doesn't do well enough for a sequel, then too bad. If it does, hallelujah, but if that second one bombs, it stops there. Legendary should not force a third sequel just to make it a cute little trilogy.
Now, if it goes to four or above films, it really all depends on what kind of stories are told along the way.
So far, we know that this first one is an origin story so Godzilla and the furture of the franchise both have room to grow. If the movie does well enough and isn't open ended, then the second movie could easily be a case of something along the lines of Godzilla's reemergence, and the creation/discovery of new enemies.
However, I will never say that creating Mechagodzilla is a good idea. It's not. I said it before and I'll say it again, there's no point in creating a robot in the shape of Godzilla. It looks cool, but that's all the practicality there is to the idea so it should not be done.
Anyway, back on track, perhaps the discovery of a new enemy. Another creature like Godzilla which grew to tremendous size either due to radiation or some other cause emerges and begins wreaking havoc. Godzilla's nemesis doesn't need more than that reason to bring about a good movie. If they want to make it more convoluted, then can, but that's all it will take to get a decent jump off point.
The problem with Godzilla is that every movie is basically going to be a continuation of the first one in that it's going to involve the concept of a new monster or some kind of new force to go against him. It's old fashioned, but it's really the only thing that works. The human race can't hold their own against him, we know that. However, again, Mechagodzilla won't work because there's no point in making a robot shaped like Godzilla. There's nothing that a mechanical Godzilla can do that a human shaped robot like the Jaegers in Pacific Rim cannot. In fact, there's less that it can do because of the limits posed by its anatomical differences.
So whatever Legendary decides to do with future sequels will have to involve more monsters because they're the only thing that will present a challenge for Godzilla. I don't personally like the Pacific Rim crossover even though I liked that movie, so if they do that I'll be more than a little disappointed in them.
My two cents.
