[jbooth] “Is this best achieved by moving the camera through space, or moving the elements through space toward and past the camera? Or is it just personal preference?”
From your description of the shot I would say you should be primarily concerned with animating the camera. Some people prefer to animate the position and point of interest of the camera. The point of interest is handy because it gives you a defined point in space that the camera is looking at, the camera automatically pans and tilts to center this point in it’s field of view.
The Point of Interest method isn’t always ideal because it can create a headache for you if you’re working with lots of keyframes.
AE defaults to bezier spatial interpolation of these keyframes and you can end up getting a ‘boomerang’ effect:
https://forums.creativecow.net/cgi-bin/page_wrapper.cgi?forumid=1&page=https://www.creativecow.net/articles/rabinowitz_aharon/boomerang_2/index.html
https://forums.creativecow.net/cgi-bin/page_wrapper.cgi?forumid=1&page=https://www.creativecow.net/articles/rabinowitz_aharon/boomerang_1/index.html
You can disable the Point of Interest by right clicking on the camera and going to Transform > Auto-Orient and changing it to ‘Off.’ In this setting you have to control all of the pans, tilts and dutch angles yourself… but some people are of the opinion that control is a good thing =)
That’s all I have to say on the subject for now… probably more than you were expecting =O