Yes, After Effects is the right application for animating Illustrator artwork.
You’ll want to learn about keyfames and Keyframe Interpolation options so that you can control the change from A to E.
You’ll want to explord the Effects that come with AE as well as 3rd party effects available for AE to be aware of how A might change into E.
You’ll want to explore how to copy and paste AI object to AE Layer Masks.
You’ll want to explore how to promote AI objects to layers at the root level of the document and then how to convert AI Layers that have been imported to AE into AE Shape Layers and then drill down into all of the Shape Layer options. (Maybe put this one at the top of your list.)
As you get better in AE and want to move more quickly between AI and AI, definitely check out Overlord (http://www.battleaxe.co/overlord/ ).
It’s also worth spending some time use on the After Effects side learning what’s possible with Masks and Shape Layers.
With all that said, you might also want to spend some time in Adobe Animate CC (formerly Adobe Flash CC). You might really enjoy the “tweening“ options for vector based artwork.
-Warren
P.S. Definatly read up on the Continuously Rasterize Layer Switch.