The process:
1 Pick the colors you want to work with. Use a darker shade of the background color for the shadow of the symbol inside.
2 Create the elements you want to use. In my case i created two circles - one for outline and one for fill. Then i created the main symbol and after that i created the rectangles and the shape for the shadow.
3 Combine the elements and make adjustments if needed.
4 Experiment with different colors positions and elements.
Here are the main and the simplified circle logo in 500x500 and 150x150 px.
"500x500 px"
"150x150 px"
Original .ai files
https://drive.google.com/open?id=1OIN8w0byY-wyawwqG-hEf1ojNz_hgAF5