I'd say you'd probably want to do this in AE, but the learning curve isn't something to ignore. To learn AE, start here. It does not work at all like a video editing program, so you'll need to get a good foundation before you charge forward into a world of frustration.
What you are talking about is just position keyframes and layers. You can do it by hand or, with a little planning, use expressions to help automate the process. The first solution you can do with a basic knowledge of spatial (animating position) and keyframes. The second will require some time and a full understanding all of the assets you have to create the composition.
Thank you both for the quick replies. I started to go through some online training and purchased an ebook (Adobe Classroom in a Book for AE CS6), so I'm off.
I'm familiar with using keyframes and layers in the Apple world of the older FCS and FCPX so the concepts are not problematic. We'll see how I do when I start working through the exercises. I agree that the learning curve will be a challenge, but AE seems to be a good tool to have in my "toolbelt."
It's great to know that there are folks like you willing to take the time and effort to help. Thanks again.