I saw the movie today, and don't worry about clicking the above link as that's not what the monster looks like. BTW, you get to see the monster quite a bit, but it's pretty irrelevant given what's going on around the monster... that's what makes the movie good.
If you like the TV series "Lost", you'll like this movie. They don't waste a lot of time going into the why's and what's of what's going on. You just get immersed into the moment and run with the charaters through to the end. Overall, I thought it was a pretty good movie.
By the way, the Cloverfield name isn't a code. It's the exit that JJ Abrams takes off the highway when he goes to work. He just needed a name and that seemed like a good one.