One of the relatively simple way to do this is to add a Trim Paths to the Contents. Click on the Contents, from the”Add” menu (little triangle right next to the Contents) select “Trim Paths”. Select “Trim multiple paths individually” option. now you can animate the Start Value from 100 to 0 and the shapes will draw one after another in the sequence they appear under Contents. You can rearrange shapes by dragging them in the list.
You can control where the individual shapes start drawing by setting the first vertex (anchor point). You can do this by selecting the path under the Shape, then selecting the desired vertex with the direct selection tool (arrow) right-clicking on it and selecting: Mask and Shape Path > Set First Vertex.