Chandler,
Welcome to the forums and thanks for your post.
At the airlines you are typically limited to flying one type of airplane at a time as airplanes all differ greatly from each other. That being said, you will bid for your aircraft type based on seniority. Typically the smaller airplanes like the 737 go to the more junior pilots while the larger airplanes like the 767 go to the more senior pilots.
At United we can change airplanes every two years. In my ten years here I have been on the 737 three different times and the 757 two different times, although I seem to change a lot more than most pilots do. For example, I just ran into a friend of mine who has been on the 757 for the last twelve years, he really enjoys his seniority on it and likes the type of flying that he is doing, so he intends on staying there for the foreseeable future.
Chris