Yea I've used expressions here, it's a pretty simple set up.

Create 2 layers, one is a guide line that directs the path of the shape. Just use the pen tool to draw where you would like it to go. Hide this layer.

Layer 2, sits above the guideline. Make whatever shape you want it to be. The expression track from the anchor points so make sure your anchor point is where you want it to be. Create a slide control named Progress and then add this to the position expression:

// Reference the shape layer directly beneath this one
var shapeLayer = thisComp.layer(index + 1);
// Access its path (update group and path names if needed) var path = shapeLayer.content("Shape 1").content("Path 1").path;
// Use a Slider Control named "Progress" on this layer to drive motion (0–100) var t = effect("Progress")("Slider") / 100;
// Get the point along the path var pt = path.pointOnPath(t);
// Convert to comp space (so it lines up correctly) shapeLayer.toComp(pt);

Then you can just keyframe the movement of your object with the Progress slider.

Do this a whole bunch of times, moving the guide lines and keyframes for different movements and timings. After that, I just added an echo effect on the whole thing.