If you use Illustrator first it can help you have a little more control of your art. So, I suggest make all your assets first in Ai first and then import them in After Effects. Then perform the scaling and add keyframes to match your animated example. Although, for something this simple you could probably also do it in Premier Pro.
If you don't know any of that stuff you need to stop what you're doing and first lookup how to use the basics of After Effects and Illustrator and then follow a tutorial the explains how to import and use the assets you created. Then research key framing. That way it will be a lot easier for you.
Things to consider: You can indeed use the tools in Ae to make the artwork. I don't recommend that though because Ae isn't really an Illustration tool. Some people have no problem doing it all in Ae.