I have the following illustration and I want to start with the dot in the middle and have the circle layers as though they are spiraling out from the dot in the very center (without using a wipe-like effect). Technically, each dot in each circle would appear in clockwise order and when a circle completes its appearance, the next outward circle of dots would beging to appear in similar fashion. Any ideas on ways to do this quicks (rather than manually animating the appearance of each circle)? If not, any other ideas on how to creatively animate the appearance of all these dots from the center dot (in a way that is not tedious)?
Card Dance, Particle Playground, Foam, CC Particle Systems, any otehr particle plug-in you can imagine, text on a spiral path, shape layer repeaters. That covers about every of the gigazillion possibilities...
If your illustrator artwork was created in the order you want the dots to appear then it's a simple matter to release the dots to layers, import the .ai file as a composition, and then sequence the layers in After Effects.
Many of your dots appear to be different but some are the same. If you want to use a particle system then you'll need to create a movie with a different dot in each frame and all of the dots lined up. The emitter would fly around a path you created leaving a single dot on every frame.
My approach would probably to create eliptical mask paths centered on each of the rings of dots, then apply stroke using all paths and stroke sequentially. The stroked layer would then be used as a track matte to reveal the dots. I think that would be the fastest solution to the problem.
Here's a project file using your screenshot that took me less than 5 minutes. The position of the masks needs a little tweaking but it should get you started.